Braid Groups

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Braid Groups

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Author : Christian Kassel
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-06-28

Braid Groups written by Christian Kassel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-28 with Mathematics categories.

In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.

Introduction To Complex Reflection Groups And Their Braid Groups

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Author : Michel Broué
language : en
Publisher: Springer
Release Date : 2010-01-28

Introduction To Complex Reflection Groups And Their Braid Groups written by Michel Broué and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-28 with Mathematics categories.

This book covers basic properties of complex reflection groups, such as characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, including the basic findings of Springer theory on eigenspaces.

Braids Links And Mapping Class Groups Am 82 Volume 82

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Author : Joan S. Birman
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

Braids Links And Mapping Class Groups Am 82 Volume 82 written by Joan S. Birman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.

Application Of Braid Groups In 2d Hall System Physics Composite Fermion Structure

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Author : Janusz Jacak
language : en
Publisher: World Scientific
Release Date : 2012-07-13

Application Of Braid Groups In 2d Hall System Physics Composite Fermion Structure written by Janusz Jacak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-13 with Science categories.

In the present treatise progress in topological approach to Hall system physics is reported, including recent achievements in graphene. The homotopy methods of braid groups turn out to be of particular convenience in order to grasp peculiarity of 2D charged systems upon magnetic field resulting in Laughlin correlations. The real progress in understanding of structure and role of composite fermions in Hall system is provided. The crucial significance of carrier mobility apart from interaction in creation of the fractional quantum Hall effect (FQHE) is described and supported by recent graphene experiments. Recent progress in FQHE field including topological insulators and optical lattices was reviewed and commented in terms of braid group approach. The braid group methods are presented from more general point of view including proposition of pure braid group application.

When The Lower Central Series Stops A Comprehensive Study For Braid Groups And Their Relatives

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Author : Jacques Darné
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-16

When The Lower Central Series Stops A Comprehensive Study For Braid Groups And Their Relatives written by Jacques Darné and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-16 with Mathematics categories.

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A Study Of Braids

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Author : Kunio Murasugi
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-06-30

A Study Of Braids written by Kunio Murasugi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-30 with Computers categories.

This book provides a comprehensive exposition of the theory of braids, beginning with the basic mathematical definitions and structures. Among the many topics explained in detail are: the braid group for various surfaces; the solution of the word problem for the braid group; braids in the context of knots and links (Alexander's theorem); Markov's theorem and its use in obtaining braid invariants; the connection between the Platonic solids (regular polyhedra) and braids; the use of braids in the solution of algebraic equations. Dirac's problem and special types of braids termed Mexican plaits are also discussed. Audience: Since the book relies on concepts and techniques from algebra and topology, the authors also provide a couple of appendices that cover the necessary material from these two branches of mathematics. Hence, the book is accessible not only to mathematicians but also to anybody who might have an interest in the theory of braids. In particular, as more and more applications of braid theory are found outside the realm of mathematics, this book is ideal for any physicist, chemist or biologist who would like to understand the mathematics of braids. With its use of numerous figures to explain clearly the mathematics, and exercises to solidify the understanding, this book may also be used as a textbook for a course on knots and braids, or as a supplementary textbook for a course on topology or algebra.

Braid Group Knot Theory And Statistical Mechanics

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Author : Mo-lin Ge
language : en
Publisher: World Scientific
Release Date : 1991-06-05

Braid Group Knot Theory And Statistical Mechanics written by Mo-lin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-05 with Science categories.

Contents:Notes on Subfactors and Statistical Mechanics (V F R Jones)Polynomial Invariants in Knot Theory (L H Kauffman)Algebras of Loops on Surfaces, Algebras of Knots, and Quantization (V G Turaev)Quantum Groups (L Faddeev et al.)Introduction to the Yang-Baxter Equation (M Jimbo)Integrable Systems Related to Braid Groups and Yang-Baxter Equation (T Kohno)The Yang-Baxter Relation: A New Tool for Knot Theory (Y Akutsu et al.)Akutsu-Wadati Link Polynomials from Feynman-Kauffman Diagrams (M-L Ge et al.)Quantum Field Theory and the Jones Polynomial (E Witten) Readership: Mathematical physicists.

Braids

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Author : A. Jon Berrick
language : en
Publisher: World Scientific
Release Date : 2010

Braids written by A. Jon Berrick and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Tutorial on the braid groups / Dale Rolfsen -- Simplicial objects and homotopy groups / Jie Wu -- Introduction to configuration spaces and their applications / Frederick R. Cohen -- Configuration spaces, braids, and robotics / Robert Ghrist -- Braids and magnetic fields / Mitchell A. Berger -- Braid group cryptography / David Garber

The Classification Of The Virtually Cyclic Subgroups Of The Sphere Braid Groups

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Author : Daciberg Lima Goncalves
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-08

The Classification Of The Virtually Cyclic Subgroups Of The Sphere Braid Groups written by Daciberg Lima Goncalves and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-08 with Mathematics categories.

This manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as enabling us to understand better the global structure of these groups, it marks an important step in the computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysis of their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another important aspect of our work is the close relationship of the braid groups with mapping class groups. This manuscript will serve as a reference for the study of braid groups of low-genus surfaces, and isaddressed to graduate students and researchers in low-dimensional, geometric and algebraic topology and in algebra. ​

Handbook Of Teichm Ller Theory

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Author : Athanase Papadopoulos
language : en
Publisher: European Mathematical Society
Release Date : 2007

Handbook Of Teichm Ller Theory written by Athanase Papadopoulos and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

This multi-volume set deals with Teichmuller theory in the broadest sense, namely, as the study of moduli space of geometric structures on surfaces, with methods inspired or adapted from those of classical Teichmuller theory. The aim is to give a complete panorama of this generalized Teichmuller theory and of its applications in various fields of mathematics. The volumes consist of chapters, each of which is dedicated to a specific topic. The volume has 19 chapters and is divided into four parts: The metric and the analytic theory (uniformization, Weil-Petersson geometry, holomorphic families of Riemann surfaces, infinite-dimensional Teichmuller spaces, cohomology of moduli space, and the intersection theory of moduli space). The group theory (quasi-homomorphisms of mapping class groups, measurable rigidity of mapping class groups, applications to Lefschetz fibrations, affine groups of flat surfaces, braid groups, and Artin groups). Representation spaces and geometric structures (trace coordinates, invariant theory, complex projective structures, circle packings, and moduli spaces of Lorentz manifolds homeomorphic to the product of a surface with the real line). The Grothendieck-Teichmuller theory (dessins d'enfants, Grothendieck's reconstruction principle, and the Teichmuller theory of the solenoid). This handbook is an essential reference for graduate students and researchers interested in Teichmuller theory and its ramifications, in particular for mathematicians working in topology, geometry, algebraic geometry, dynamical systems and complex analysis. The authors are leading experts in the field.