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Intelligence Of Low Dimensional Topology 2006
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Book Synopsis Intelligence Of Low Dimensional Topology 2006 by : J Scott Carter
Download or read book Intelligence Of Low Dimensional Topology 2006 written by J Scott Carter and published by World Scientific. This book was released on 2007-05-29 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the contributions from the international conference “Intelligence of Low Dimensional Topology 2006,” which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.
Book Synopsis Intelligence of Low Dimensional Topology 2006 by : J. Scott Carter
Download or read book Intelligence of Low Dimensional Topology 2006 written by J. Scott Carter and published by World Scientific. This book was released on 2007 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers the contributions from the international conference ?Intelligence of Low Dimensional Topology 2006,? which took place in Hiroshima in 2006. The aim of this volume is to promote research in low dimensional topology with the focus on knot theory and related topics. The papers include comprehensive reviews and some latest results.
Book Synopsis Knots, Low-Dimensional Topology and Applications by : Colin C. Adams
Download or read book Knots, Low-Dimensional Topology and Applications written by Colin C. Adams and published by Springer. This book was released on 2019-06-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.
Book Synopsis New Ideas In Low Dimensional Topology by : Vassily Olegovich Manturov
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.
Book Synopsis Encyclopedia of Knot Theory by : Colin Adams
Download or read book Encyclopedia of Knot Theory written by Colin Adams and published by CRC Press. This book was released on 2021-02-10 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory
Book Synopsis Knots and Primes by : Masanori Morishita
Download or read book Knots and Primes written by Masanori Morishita and published by Springer Nature. This book was released on with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Knot Theory and Its Applications by : Krishnendu Gongopadhyay
Download or read book Knot Theory and Its Applications written by Krishnendu Gongopadhyay and published by American Mathematical Soc.. This book was released on 2016-09-21 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10–20, 2013, at IISER Mohali, India. The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas. This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.
Book Synopsis Surface-Knots in 4-Space by : Seiichi Kamada
Download or read book Surface-Knots in 4-Space written by Seiichi Kamada and published by Springer. This book was released on 2017-03-28 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory volume provides the basics of surface-knots and related topics, not only for researchers in these areas but also for graduate students and researchers who are not familiar with the field.Knot theory is one of the most active research fields in modern mathematics. Knots and links are closed curves (one-dimensional manifolds) in Euclidean 3-space, and they are related to braids and 3-manifolds. These notions are generalized into higher dimensions. Surface-knots or surface-links are closed surfaces (two-dimensional manifolds) in Euclidean 4-space, which are related to two-dimensional braids and 4-manifolds. Surface-knot theory treats not only closed surfaces but also surfaces with boundaries in 4-manifolds. For example, knot concordance and knot cobordism, which are also important objects in knot theory, are surfaces in the product space of the 3-sphere and the interval.Included in this book are basics of surface-knots and the related topics of classical knots, the motion picture method, surface diagrams, handle surgeries, ribbon surface-knots, spinning construction, knot concordance and 4-genus, quandles and their homology theory, and two-dimensional braids.
Book Synopsis Quandles and Topological Pairs by : Takefumi Nosaka
Download or read book Quandles and Topological Pairs written by Takefumi Nosaka and published by Springer. This book was released on 2017-11-20 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteemed quandle theory is in mathematics, and it constitutes a crash course for studying quandles.More precisely, this work emphasizes the fresh perspective that quandle theory can be useful for the study of low-dimensional topology (e.g., knot theory) and relative objects with symmetry. The direction of research is summarized as “We shall thoroughly (re)interpret the previous studies of relative symmetry in terms of the quandle”. The perspectives contained herein can be summarized by the following topics. The first is on relative objects G/H, where G and H are groups, e.g., polyhedrons, reflection, and symmetric spaces. Next, central extensions of groups are discussed, e.g., spin structures, K2 groups, and some geometric anomalies. The third topic is a method to study relative information on a 3-dimensional manifold with a boundary, e.g., knot theory, relative cup products, and relative group cohomology.For applications in topology, it is shown that from the perspective that some existing results in topology can be recovered from some quandles, a method is provided to diagrammatically compute some “relative homology”. (Such classes since have been considered to be uncomputable and speculative). Furthermore, the book provides a perspective that unifies some previous studies of quandles.The former part of the book explains motivations for studying quandles and discusses basic properties of quandles. The latter focuses on low-dimensional topology or knot theory. Finally, problems and possibilities for future developments of quandle theory are posed.
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 Applications of Contact Geometry and Topology in Physics by : Arkady L Kholodenko
Download or read book Applications of Contact Geometry and Topology in Physics written by Arkady L Kholodenko and published by World Scientific. This book was released on 2013-05-03 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although contact geometry and topology is briefly discussed in V I Arnol'd's book “Mathematical Methods of Classical Mechanics ”(Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges “An Introduction to Contact Topology” (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph “Contact Geometry and Nonlinear Differential Equations” (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau–Lifshitz (L–L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L–L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L–L course some problems/exercises are formulated along the way and, again as in the L–L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L–L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text. Contents:Motivation and BackgroundFrom Ideal Magnetohydrodynamics to String and Knot TheoryAll About and Around Woltjer's TheoremTopologically Massive Gauge Theories and Force-Free FieldsContact Geometry and PhysicsSub-Riemannian Geometry, Heisenberg Manifolds and Quantum Mechanics of Landau LevelsAbrikosov Lattices, TGB Phases in Liquid Crystals and Heisenberg GroupSub-Riemannian Geometry, Spin Dynamics and Quantum-Classical Optimal ControlFrom Contact Geometry to Contact TopologyClosing Remarks:The Unreasonable Effectivenessof Contact Geometry and Topology in Physical SciencesAppendices:Heisenberg Group in the Context of Sub-Riemannian Geometry and Optimal ControlSub-Riemannian Dynamics of Josephson JunctionsQuantum Computers and Quantum Random WalksThe Measurement Protocol. Geometry and Topology of Entanglements Readership: Students in applied mathematics and theoretical physics. Keywords:Force-Free Fields;Contact and Sub-Riemannian Geometry;Optimal Control;Theoretical PhysicsKey Features:This book is the world's first book on contact/sub-Riemannian geometry and topology for physicistsUnlike books discussing mathematical methods for physicists, this book discusses physical problems first and only then uses new mathematics to solve these problems. Problems are selected from practically all branches of theoretical physicsThis is done with the purpose of demonstrating that contact geometry should be looked upon as a universal language/technical tool of theoretical physicsReviews: “This book is written in the style of the well-known Landau-Lifshitz multivolume course in theoretical physics and its prime goal, as the author puts it, is to show the diversity of applications of contact geometry and topology. I enjoyed reading this book, in which the author allows readers to see for themselves “the same forest behind different kinds of trees”. I strongly recommend this book to interested readers.” MathSciNet
Book Synopsis An Invitation to Knot Theory by : Heather A. Dye
Download or read book An Invitation to Knot Theory written by Heather A. Dye and published by CRC Press. This book was released on 2018-09-03 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra. The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.
Book Synopsis Topological Library: Spectral sequences in topology by : Sergeĭ Petrovich Novikov
Download or read book Topological Library: Spectral sequences in topology written by Sergeĭ Petrovich Novikov and published by World Scientific. This book was released on 2007 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in 1950-60s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated "singular homologies of fiber spaces
Book Synopsis Topological Library by : S P Novikov
Download or read book Topological Library written by S P Novikov and published by World Scientific. This book was released on 2012-07-25 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final volume of the three-volume edition, this book features classical papers on algebraic and differential topology published in the 1950s–1960s. The partition of these papers among the volumes is rather conditional. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950. That is, from Serre's celebrated “singular homologies of fiber spaces.” Contents:Singular Homology of Fiber Spaces (J-P Serre)Homotopy Groups and Classes of Abelian Groups (J-P Serre)Cohomology Modulo 2 of Eilenberg–MacLane Complexes (J-P Serre)On Cohomology of Principal Fiber Bundles and Homogeneous Spaces of Compact Lie Groups (A Borel)Cohomology Mod 2 of Some Homogeneous Spaces (A Borel)The Steenrod Algebra and Its Dual (J Milnor)On the Structure and Applications of the Steenrod Algebra (J F Adams)Vector Bundles and Homogeneous Spaces (M F Atiyah and F Hirzebruch)The Methods of Algebraic Topology from Viewpoint of Cobordism Theory (S P Novikov) Readership: Researchers in algebraic topology, its applications, and history of topology. Keywords:Topology;Homeomorphism;Fundamental Group;Smooth Manifold;Homology;Homotopy;Fiber Spaces;Vector Bundles;Characteristic Classes;Homogeneous Spaces;Cobordism;Steenrod AlgebraKey Features:Serves as a tool in learning classical algebraic topologyAn essential book for topologistsReviews: "It is utmost useful to have these (interrelated) classics gathered together in one volume. This facilitates the study of the originals considerably, all the more as numerous editorial hints provide additional guidance. In this regard, the entire edition represents an invaluable source book for both students and researchers in the field." Zentralblatt MATH "This is a nice volume that should not be missing in any Mathematics Library." European Mathematical Society
Book Synopsis Spectral Analysis in Geometry and Number Theory by : Motoko Kotani
Download or read book Spectral Analysis in Geometry and Number Theory written by Motoko Kotani and published by American Mathematical Soc.. This book was released on 2009 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outgrowth of an international conference in honor of Toshikazu Sunada on the occasion of his sixtieth birthday. The conference took place at Nagoya University, Japan, in 2007. Sunada's research covers a wide spectrum of spectral analysis, including interactions among geometry, number theory, dynamical systems, probability theory and mathematical physics. Readers will find papers on trace formulae, isospectral problems, zeta functions, quantum ergodicity, random waves, discrete geometric analysis, value distribution, and semiclassical analysis. This volume also contains an article that presents an overview of Sunada's work in mathematics up to the age of sixty.
Book Synopsis Virtual Knots by : Vasilii Olegovich Manturov
Download or read book Virtual Knots written by Vasilii Olegovich Manturov and published by World Scientific. This book was released on 2012 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory.Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose, it became clear that classical knot theory was a small integral part of a larger theory, and studying properties of virtual knots helped one understand better some aspects of classical knot theory and encouraged the study of further problems. Virtual knot theory finds its applications in classical knot theory. Virtual knot theory occupies an intermediate position between the theory of knots in arbitrary three-manifold and classical knot theory.In this book we present the latest achievements in virtual knot theory including Khovanov homology theory and parity theory due to V O Manturov and graph-link theory due to both authors. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams.Graph-links can be treated as OC diagramless knot theoryOCO: such OC linksOCO have crossings, but they do not have arcs connecting these crossings. It turns out, however, that to graph-links one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory.
Book Synopsis Introductory Lectures on Knot Theory by : Louis H. Kauffman
Download or read book Introductory Lectures on Knot Theory written by Louis H. Kauffman and published by World Scientific. This book was released on 2012 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.
