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Representing 3 Manifolds By Filling Dehn Surfaces
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Book Synopsis Representing 3-manifolds By Filling Dehn Surfaces by : Ruben Vigara Benito
Download or read book Representing 3-manifolds By Filling Dehn Surfaces written by Ruben Vigara Benito and published by World Scientific. This book was released on 2016-03-11 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the beautiful and deep subject of filling Dehn surfaces in the study of topological 3-manifolds. This book presents, for the first time in English and with all the details, the results from the PhD thesis of the first author, together with some more recent results in the subject. It also presents some key ideas on how these techniques could be used on other subjects.Representing 3-Manifolds by Filling Dehn Surfaces is mostly self-contained requiring only basic knowledge on topology and homotopy theory. The complete and detailed proofs are illustrated with a set of more than 600 spectacular pictures, in the tradition of low-dimensional topology books. It is a basic reference for researchers in the area, but it can also be used as an advanced textbook for graduate students or even for adventurous undergraduates in mathematics. The book uses topological and combinatorial tools developed throughout the twentieth century making the volume a trip along the history of low-dimensional topology.
Book Synopsis Representing 3-Manifolds by Filling Dehn Surfaces by : Rubén Vigara
Download or read book Representing 3-Manifolds by Filling Dehn Surfaces written by Rubén Vigara and published by . This book was released on 2016 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to 3-Manifolds by : Jennifer Schultens
Download or read book Introduction to 3-Manifolds written by Jennifer Schultens and published by American Mathematical Soc.. This book was released on 2014-05-21 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology. The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for 3-manifolds, and provides an overview of knot theory. It then continues with more specialized topics by briefly considering triangulations of 3-manifolds, normal surface theory, and Heegaard splittings. The book finishes with a discussion of topics relevant to viewing 3-manifolds via the curve complex. With about 250 figures and more than 200 exercises, this book can serve as an excellent overview and starting point for the study of 3-manifolds.
Book Synopsis Foliations and the Geometry of 3-Manifolds by : Danny Calegari
Download or read book Foliations and the Geometry of 3-Manifolds written by Danny Calegari and published by Oxford University Press on Demand. This book was released on 2007-05-17 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference, aimed at research topologists, gives an exposition of the 'pseudo-Anosov' theory of foliations of 3-manifolds. This theory generalizes Thurston's theory of surface automorphisms and reveals an intimate connection between dynamics, geometry and topology in 3 dimensions. Significant themes returned to throughout the text include the importance of geometry, especially the hyperbolic geometry of surfaces, the importance of monotonicity, especially in1-dimensional and co-dimensional dynamics, and combinatorial approximation, using finite combinatorical objects such as train-tracks, branched surfaces and hierarchies to carry more complicated continuous objects.
Book Synopsis Surgery on Contact 3-manifolds and Stein Surfaces by : Burak Ozbagci
Download or read book Surgery on Contact 3-manifolds and Stein Surfaces written by Burak Ozbagci and published by . This book was released on 2004 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about an investigation of recent developments in the field of sympletic and contact structures on four and three dimensional manifolds, respectively, from a topologist's point of view. The level of the book is appropriate for advanced graduate students.
Download or read book 3-Manifolds written by John Hempel and published by American Mathematical Soc.. This book was released on 2004-11-02 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A careful and systematic development of the theory of the topology of 3-manifolds, focusing on the critical role of the fundamental group in determining the topological structure of a 3-manifold ... self-contained ... one can learn the subject from it ... would be very appropriate as a text for an advanced graduate course or as a basis for a working seminar. --Mathematical Reviews For many years, John Hempel's book has been a standard text on the topology of 3-manifolds. Even though the field has grown tremendously, the book remains one of the best and most popular introductions to the subject. The theme of this book is the role of the fundamental group in determining the topology of a given 3-manifold. The essential ideas and techniques are covered in the first part of the book: Heegaard splittings, connected sums, the loop and sphere theorems, incompressible surfaces, free groups, and so on. Along the way, many useful and insightful results are proved, usually in full detail. Later chapters address more advanced topics, including Waldhausen's theorem on a class of 3-manifolds that is completely determined by its fundamental group. The book concludes with a list of problems that were unsolved at the time of publication. Hempel's book remains an ideal text to learn about the world of 3-manifolds. The prerequisites are few and are typical of a beginning graduate student. Exercises occur throughout the text.
Book Synopsis Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences by : Alexey Stakhov
Download or read book Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science-volume 3:the "Golden" Paradigm Of Modern Science: Prerequisite For The "Golden" Revolution In Mathematics,computer Science,and Theoretical Natural Sciences written by Alexey Stakhov and published by World Scientific. This book was released on 2020-09-03 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Book Synopsis Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic by : Alexey Stakhov
Download or read book Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic's And Ternary Mirror-symmetrical Arithmetic written by Alexey Stakhov and published by World Scientific. This book was released on 2020-09-03 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Book Synopsis On Complementarity: A Universal Organizing Principle by : Jack Shulman Avrin
Download or read book On Complementarity: A Universal Organizing Principle written by Jack Shulman Avrin and published by World Scientific. This book was released on 2021-08-06 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is not uncommon for the Principle of Complementarity to be invoked in either Science or Philosophy, viz. the ancient oriental philosophy of Yin and Yang whose symbolic representation is portrayed on the cover of the book. Or Niels Bohr's use of it as the basis for the so-called Copenhagen interpretation of Quantum Mechanics. This book arose as an outgrowth of the author's previous book entitled 'Knots, Braids and Moebius Strips,' published by World Scientific in 2015, wherein the Principle itself was discovered to be expressible as a simple 2x2 matrix that summarizes the algebraic essence of both the well-known Microbiology of DNA and the author's version of the elementary particles of physics. At that point, the possibility of an even wider utilization of that expression of Complementarity arose.The current book, features Complementarity, in which the matrix algebra is extended to characterize not only DNA itself but the well-known process of its replication, a most gratifying outcome. The book then goes on to explore Complementarity, with and without its matrix expression, as it occurs, not only in much of physics but in its extension to cosmology as well.
Book Synopsis Board Games: Throughout The History And Multidimensional Spaces by : Kyppo Jorma
Download or read book Board Games: Throughout The History And Multidimensional Spaces written by Kyppo Jorma and published by World Scientific. This book was released on 2019-07-08 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this richly illustrated book, Dr Jorma Kyppö explores the history of board games dating back to Ancient Egypt, Mesopotamia, India and China. He provides a description of the evolution and various interpretations of chess. Furthermore, the book offers the study of the old Celtic and Viking board games and the old Hawaiian board game Konane, as well as a new hypothesis about the interpretation of the famous Cretan Phaistos Disk. Descriptions of several chess variations, including some highlights of the game theory and tiling in different dimensions, are followed by a multidimensional symmetrical n-person strategy game model, based on chess. Final chapter (Concluding remarks) offers the new generalizations of the Euler-Poincare's Characteristic, Pi and Fibonacci sequence.
Book Synopsis Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids by : Alexey Stakhov
Download or read book Mathematics Of Harmony As A New Interdisciplinary Direction And "Golden" Paradigm Of Modern Science - Volume 1: The Golden Section, Fibonacci Numbers, Pascal Triangle, And Platonic Solids written by Alexey Stakhov and published by World Scientific. This book was released on 2020-05-05 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume I is the first part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and 'Golden' Paradigm of Modern Science. 'Mathematics of Harmony' rises in its origin to the 'harmonic ideas' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the 'Universe Harmony,' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the 'Mathematics of Harmony,' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet's formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Book Synopsis Polynomial One-cocycles For Knots And Closed Braids by : Fiedler Thomas
Download or read book Polynomial One-cocycles For Knots And Closed Braids written by Fiedler Thomas and published by World Scientific. This book was released on 2019-08-27 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, knot theory deals with diagrams of knots and the search of invariants of diagrams which are invariant under the well known Reidemeister moves. This book goes one step beyond: it gives a method to construct invariants for one parameter famillies of diagrams and which are invariant under 'higher' Reidemeister moves. Luckily, knots in 3-space, often called classical knots, can be transformed into knots in the solid torus without loss of information. It turns out that knots in the solid torus have a particular rich topological moduli space. It contains many 'canonical' loops to which the invariants for one parameter families can be applied, in order to get a new sort of invariants for classical knots.
Book Synopsis Mereon Matrix, The: Everything Connected Through (K)nothing by : Kauffman Louis H
Download or read book Mereon Matrix, The: Everything Connected Through (K)nothing written by Kauffman Louis H and published by World Scientific. This book was released on 2018-06-12 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this richly illustrated book, the contributors describe the Mereon Matrix, its dynamic geometry and topology. Through the definition of eleven First Principles, it offers a new perspective on dynamic, whole and sustainable systems that may serve as a template information model. This template has been applied to a set of knowledge domains for verification purposes: pre-life-evolution, human molecular genetics and biological evolution, as well as one social application on classroom management. The importance of the book comes in the following ways: The dynamics of the geometry unites all Platonic and Kepler Solids into one united structure and creates 11 unique trefoil knots. Its topology is directly related to the dynamics of the polyhedra. The Mereon Matrix is an approach to the unification of knowledge that relies on whole systems modelling. it is a framework charting the emergence of the Platonic and Kepler solids in a sequential, emergent growth process that describes a non-linear whole system, and includes a process of 'breathing' as well as multiplying ('birthing'); This dynamic/kinematic structure provides insight and a new approach to General Systems Theory and non-linear science, evolving through a new approach to polyhedral geometry. A set of 11 First Principles is derived from the structure, topology and dynamics of the Mereon Matrix, which serve well as a template information model. The Mereon Matrix is related to a large number of systems, physical, mathematical, and philosophical, and in linking these systems, provides access to new relationships among them by combining geometry with process thinking. The new perspective on systems is hypothesized as universal -- this is, applicable in all areas of science, natural and social. Such applicability has been demonstrated for applications as diverse as pre-life evolution, biological evolution and human molecular genetics, as well as a classroom management system for the educational system. Care has been taken to use images and languaging that are understandable across domains, connecting diverse disciplines, while making this complex system easily accessible. Contents: Prologues: Sustainability: Mathematical Elegance, Solid Science and Social Grace (L Dennis and L H Kauffman) Lynnclaire Dennis & R Buckminster Fuller Investigation (R W Gray) The Matrix We Call Mereon (L H Kauffman) First Things First: Building on the Known: A Quintessential Jitterbug (L Dennis, J Brender McNair, N J Woolf and L H Kauffman) Methodology (J Brender McNair and L Dennis) Philosophical Thoughts and Thinking Aloud Allowed (L Dennis) Belonging -- Education as Transformation (L Dennis) Meme, Pattern and Perspective (L Dennis, N J Woolf and L H Kauffman) Including and Beyond the Point: The Context -- Form Informing Function (L Dennis, J Brender McNair, N J Woolf and L H Kauffman) Flow and Scale (L Dennis and L H Kauffman) The Core -- Sharp Distinctions to Elegant Curves (L Dennis and L H Kauffman) Connections, Ligatures and Knots: Mereon Thoughts -- Knots and Beyond (L H Kauffman) The Mereon Trefoil -- Asymmetrical with Perfect Symmetry (L Dennis) Applying Mereon to Knowledge Domains: Exploring the Mereon Matrix (and Beyond) with the CymaScope Technology (L Dennis and P McNair) The Origin of Matter: Life, Learning and Survival (N J Woolf and L Dennis) ATCG -- An Applied Theory for Human MoleCular Genetics (J Brender McNair, P McNair,
Book Synopsis New Horizons For Second-order Cybernetics by : Muller Karl H
Download or read book New Horizons For Second-order Cybernetics written by Muller Karl H and published by World Scientific. This book was released on 2017-09-15 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: In almost 60 articles this book reviews the current state of second-order cybernetics and investigates which new research methods second-order cybernetics can offer to tackle wicked problems in science and in society. The contributions explore its application to both scientific fields (such as mathematics, psychology and consciousness research) and non-scientific ones (such as design theory and theater science). The book uses a pluralistic, multifaceted approach to discuss these applications: Each main article is accompanied by several commentaries and author responses, which together allow the reader to discover further perspectives than in the original article alone. This procedure shows that second-order cybernetics is already on its way to becoming an idea shared by many researchers in a variety of disciplines. Contents: Prologue: A Brief History of (Second-Order) Cybernetics (Louis H Kauffman & Stuart A Umpleb)Mapping the Varieties of Second-Order Cybernetics (Karl H Müller & Alexander Riegle)Part I: Exploring Second-Order Cybernetics and Its Fivefold Agenda: Second-Order Cybernetics as a Fundamental Revolution in Science (Stuart A Umpleby)Obstacles and Opportunities in the Future of Second-Order Cybernetics and Other Compatible Methods (Allenna Leonard)Connecting Second-Order Cybernetics' Revolution with Genetic Epistemology (Gastón Becerra)Shed the Name to Find Second-Order Success: Renaming Second-Order Cybernetics to Rescue its Essence (Michael R Lissack)Beware False Dichotomies (Peter A Cariani)Second-Order Cybernetics Needs a Unifying Methodology (Thomas R Flanagan)Viva the Fundamental Revolution! Confessions of a Case Writer (T Grandon Gill)Author's Response: Struggling to Define an Identity for Second-Order Cybernetics (Stuart A Umpleby)Cybernetics, Reflexivity and Second-Order Science (Louis H Kauffman)Remarks From a Continental Philosophy Point of View (Tatjana Schönwälder-Kuntze)Finally Understanding Eigenforms (Michael R Lissack)Eigenforms, Coherence, and the Imaginal (Arthur M Collings)Conserving the Disposition for Wonder (Kathleen Forsythe)Author's Response: Distinction, Eigenform and the Epistemology of the Imagination (Louis H Kauffman)Cybernetic Foundations for Psychology (Bernard Scott)Wielding the Cybernetic Scythe in the Blunting Undergrowth of Psychological Confusion (Vincent Kenny)To What Extent Can Second-Order Cybernetics Be a Foundation for Psychology? (Marcelo Arnold-Cathalifaud & Daniela Thumala-Dockendorff)The Importance — and the Difficulty — of Moving Beyond Linear Causality (Robert J Martin)Obstacles to Cybernetics Becoming a Conceptual Framework and Metanarrative in the Psychologies (Philip Baron)The Social and the Psychological: Conceptual Cybernetic Unification vs Disciplinary Analysis? (Eva Buchinger)Second Thoughts on Cybernetic Unifications (Tilia Stingl de Vasconcelos Guedes)Cybernetics and Synergetics as Foundations for Complex Approach Towards Complexities of Life (Lea Šugman Bohinc)Author's Response: On Becoming and Being a Cybernetician (Bernard Scott)Consciousness as Self-Description in Differences (Diana Gasparyan)On the Too Often Overlooked Complexity of the Tension between Subject and Object (Yochai Ataria)Where Is Consciousness? (Urban Kordeš)Theorizing Agents: Their Games, Hermeneutical Tools and Epistemic Resources (Konstantin Pavlov-Pinus)How
Book Synopsis Quipu: Decorated Permutation Representations Of Finite Groups by : Yongju Bae
Download or read book Quipu: Decorated Permutation Representations Of Finite Groups written by Yongju Bae and published by World Scientific. This book was released on 2024-06-27 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.
Book Synopsis Scientific Legacy Of Professor Zbigniew Oziewicz: Selected Papers From The International Conference "Applied Category Theory Graph-operad-logic" by : Hilda Maria Colin Garcia
Download or read book Scientific Legacy Of Professor Zbigniew Oziewicz: Selected Papers From The International Conference "Applied Category Theory Graph-operad-logic" written by Hilda Maria Colin Garcia and published by World Scientific. This book was released on 2023-09-27 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dedicated to the memory of the late Professor Zbigniew Oziewicz from Universidad Nacional Autónoma de México, the book consists of papers on a wide variety of topics related to the work of Professor Oziewicz, which were presented at the special conference on Graph-Operads-Logic (GOL 2021), selected through peer review to promote his scientific legacy.Professor Oziewicz was a great enthusiast and supporter of category theory and its applications in physics, as well as in various areas of mathematics (topology, noncommutative geometry, etc.). In particular, he made significant contributions to the theory of Frobenius algebras, which now are becoming more important due to their connection with topological quantum field theories that are used in mathematical physics and in quantum topology. Professor Oziewicz was a great and very generous teacher, who immersed his students in the beautiful ideas of category theory as well as mathematical physics and computation. It was his idea to start a series of conferences under the title Graphs-Operads-Logic, most of them held in Mexico, with some of them in the USA, which were a great platform to discuss various ideas connected with category theory and its various applications, and to make friends with other scientists. Despite his passing, the GOL 2021 conference is included in this series to pay tribute to his many contributions to diverse areas of science.The book is laid out in twelve main topics where we can find relevant works from distinguished experts.
Book Synopsis The Geometry Of The Universe by : Colin Rourke
Download or read book The Geometry Of The Universe written by Colin Rourke and published by World Scientific. This book was released on 2021-06-03 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cosmology, the study of the universe, arouses a great deal of public interest, with serious articles both in the scientific press and in major newspapers, with many of the theories and concepts (e.g. the 'big bang' and 'black holes') discussed, often in great depth.Accordingly the book is divided into three parts:Part 1 is readable (and understandable) by anyone with a nodding acquaintance with the basic language of cosmology: events, lights paths, galaxies, black holes and so on. It covers the whole story of the book in a way as untechnical as possible given the scope of the topics covered.Part 2 covers the same ground again but with enough technical details to satisfy a reader with basic knowledge of mathematics and/or physics.Part 3 consists of appendices which are referred to in the other parts and which also contain the highly technical material omitted from Section 2.
