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Author : Vasiliĭ Olegovich Manturov
Publisher :
ISBN 13 : 9789811220128
Total Pages : 357 pages
Book Rating : 4.2/5 (21 download)
Download or read book Invariants and Pictures written by Vasiliĭ Olegovich Manturov and published by . This book was released on 2020 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vassily Olegovich Manturov
Publisher : World Scientific
ISBN 13 : 9811220131
Total Pages : 387 pages
Book Rating : 4.8/5 (112 download)
Download or read book Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory written by Vassily Olegovich Manturov and published by World Scientific. This book was released on 2020-04-22 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.
Author : Vassily Olegovich Manturov
Publisher : World Scientific
ISBN 13 : 9814630632
Total Pages : 540 pages
Book Rating : 4.8/5 (146 download)
Download or read book New Ideas In Low Dimensional Topology written by Vassily Olegovich Manturov and published by World Scientific. This book was released on 2015-01-27 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of a selection of articles devoted to new ideas and developments in low dimensional topology. Low dimensions refer to dimensions three and four for the topology of manifolds and their submanifolds. Thus we have papers related to both manifolds and to knotted submanifolds of dimension one in three (classical knot theory) and two in four (surfaces in four dimensional spaces). Some of the work involves virtual knot theory where the knots are abstractions of classical knots but can be represented by knots embedded in surfaces. This leads both to new interactions with classical topology and to new interactions with essential combinatorics.
Author : V. V. Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 0821808982
Total Pages : 239 pages
Book Rating : 4.8/5 (218 download)
Download or read book Knots, Links, Braids, and 3-manifolds written by V. V. Prasolov and published by American Mathematical Soc.. This book was released on 1997 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. It emphasizes the geometric aspects of the theory and treats topics such as braids, homeomorphisms of surfaces, surgery of 3-manifolds (Kirby calculus), and branched coverings. This attractive geometric material, interesting in itself yet not previously gathered in book form, constitutes the basis of the last two chapters, where the Jones-Witten invariants are constructed via the rigorous skein algebra approach (mainly due to the Saint Petersburg school). Unlike several recent monographs, where all of these invariants are introduced by using the sophisticated abstract algebra of quantum groups and representation theory, the mathematical prerequisites are minimal in this book. Numerous figures and problems make it suitable as a course text and for self-study.
Author : Thomas Fiedler
Publisher : World Scientific
ISBN 13 : 9811263019
Total Pages : 341 pages
Book Rating : 4.8/5 (112 download)
Download or read book One-cocycles And Knot Invariants written by Thomas Fiedler and published by World Scientific. This book was released on 2023-01-04 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: One-Cocycles and Knot Invariants is about classical knots, i.e., smooth oriented knots in 3-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used to construct combinatorial 1-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and the longitude of the knot. The combinatorial 1-cocycles are therefore lifts of the well-known Conway polynomial of knots, and they can be calculated in polynomial time. The 1-cocycles can distinguish loops consisting of knot diagrams in the moduli space up to homology. They give knot invariants when they are evaluated on canonical loops in the connected components of the moduli space. They are a first candidate for numerical knot invariants which can perhaps distinguish the orientation of knots.
Author : Hilda Maria Colin Garcia
Publisher : World Scientific
ISBN 13 : 981127116X
Total Pages : 771 pages
Book Rating : 4.8/5 (112 download)
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.
Author : Jay Kappraff
Publisher : World Scientific
ISBN 13 : 9811219729
Total Pages : 368 pages
Book Rating : 4.8/5 (112 download)
Download or read book Geometric Foundations Of Design: Old And New written by Jay Kappraff and published by World Scientific. This book was released on 2021-03-05 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is meant to serve either as a textbook for an interdisciplinary course in Mathematics of Design, or as a trade book for designers. It will also be of interest for people interested in recreational mathematics showing the connection between mathematics and design. Topics from the book can also be adapted for use in pre-college mathematics. Each chapter will provide the user with ideas that can be incorporated in a design. Background materials will be provided to show the reader the mathematical principles that lie behind the designs.
Author : Colin Rourke
Publisher : World Scientific
ISBN 13 : 9811233888
Total Pages : 274 pages
Book Rating : 4.8/5 (112 download)
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.
Author : Louis H Kauffman
Publisher : World Scientific
ISBN 13 : 9811247447
Total Pages : 944 pages
Book Rating : 4.8/5 (112 download)
Download or read book Laws Of Form: A Fiftieth Anniversary written by Louis H Kauffman and published by World Scientific. This book was released on 2023-01-09 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Laws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8-10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019.
Author : Alexey Stakhov
Publisher : World Scientific
ISBN 13 : 9811213518
Total Pages : 244 pages
Book Rating : 4.8/5 (112 download)
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.
Author : Alexey Stakhov
Publisher : World Scientific
ISBN 13 : 9811213488
Total Pages : 331 pages
Book Rating : 4.8/5 (112 download)
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.
Author : Jack Shulman Avrin
Publisher : World Scientific
ISBN 13 : 9813278994
Total Pages : 281 pages
Book Rating : 4.8/5 (132 download)
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.
Author : R. Brown
Publisher : Cambridge University Press
ISBN 13 : 0521281466
Total Pages : 261 pages
Book Rating : 4.5/5 (212 download)
Download or read book Low-Dimensional Topology written by R. Brown and published by Cambridge University Press. This book was released on 1982-05-20 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of the proceedings of a conference held at the University College of North Wales (Bangor) in July of 1979. It assembles research papers which reflect diverse currents in low-dimensional topology. The topology of 3-manifolds, hyperbolic geometry and knot theory emerge as major themes. The inclusion of surveys of work in these areas should make the book very useful to students as well as researchers.
Author : Paul Latiolais
Publisher : Springer
ISBN 13 : 3540462961
Total Pages : 215 pages
Book Rating : 4.5/5 (44 download)
Download or read book Topology and Combinatorial Group Theory written by Paul Latiolais and published by Springer. This book was released on 2006-11-14 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates the lively interaction between algebraic topology, very low dimensional topology and combinatorial group theory. Many of the ideas presented are still in their infancy, and it is hoped that the work here will spur others to new and exciting developments. Among the many techniques disussed are the use of obstruction groups to distinguish certain exact sequences and several graph theoretic techniques with applications to the theory of groups.
Author : David N. Yetter
Publisher : World Scientific
ISBN 13 : 9810244436
Total Pages : 238 pages
Book Rating : 4.8/5 (12 download)
Download or read book Functorial Knot Theory written by David N. Yetter and published by World Scientific. This book was released on 2001 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory.This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations.
Author : Cynthia Hog-Angeloni
Publisher : Cambridge University Press
ISBN 13 : 0521447003
Total Pages : 428 pages
Book Rating : 4.5/5 (214 download)
Download or read book Two-Dimensional Homotopy and Combinatorial Group Theory written by Cynthia Hog-Angeloni and published by Cambridge University Press. This book was released on 1993-12-09 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.
Author : Samuel J. Lomonaco
Publisher : American Mathematical Soc.
ISBN 13 : 0821850164
Total Pages : 346 pages
Book Rating : 4.8/5 (218 download)
Download or read book Low Dimensional Topology written by Samuel J. Lomonaco and published by American Mathematical Soc.. This book was released on 1983 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume arose from a special session on Low Dimensional Topology organized and conducted by Dr. Lomonaco at the American Mathematical Society meeting held in San Francisco, California, January 7-11, 1981.
