Properties Of Closed 3 Braids And Braid Representations Of Links PDF Download
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Author | : Alexander Stoimenow |
Publisher | : Springer |
Total Pages | : 115 |
Release | : 2017-11-29 |
Genre | : Mathematics |
ISBN | : 3319681494 |
Download Properties of Closed 3-Braids and Braid Representations of Links Book in PDF, ePub and Kindle
This book studies diverse aspects of braid representations via knots and links. Complete classification results are illustrated for several properties through Xu’s normal 3-braid form and the Hecke algebra representation theory of link polynomials developed by Jones. Topological link types are identified within closures of 3-braids which have a given Alexander or Jones polynomial. Further classifications of knots and links arising by the closure of 3-braids are given, and new results about 4-braids are part of the work. Written with knot theorists, topologists,and graduate students in mind, this book features the identification and analysis of effective techniques for diagrammatic examples with unexpected properties.
Author | : Joan S. Birman |
Publisher | : Princeton University Press |
Total Pages | : 244 |
Release | : 1974 |
Genre | : Crafts & Hobbies |
ISBN | : 9780691081496 |
Download Braids, Links, and Mapping Class Groups Book in PDF, ePub and Kindle
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.
Author | : Colin C. Adams |
Publisher | : Springer |
Total Pages | : 476 |
Release | : 2019-06-26 |
Genre | : Mathematics |
ISBN | : 3030160319 |
Download Knots, Low-Dimensional Topology and Applications Book in PDF, ePub and Kindle
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.
Author | : Kunio Murasugi |
Publisher | : American Mathematical Soc. |
Total Pages | : 122 |
Release | : 1974-12-31 |
Genre | : Mathematics |
ISBN | : 0821818511 |
Download On Closed 3-Braids Book in PDF, ePub and Kindle
The relationships between the conjugate classes of 3-braids and the link types of their closure are investigated, and it is shown that the product link type of closed pure 3-braid is determined by its conjugate class.
Author | : Joan S. Birman |
Publisher | : Princeton University Press |
Total Pages | : 237 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881420 |
Download Braids, Links, and Mapping Class Groups. (AM-82), Volume 82 Book in PDF, ePub and Kindle
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.
Author | : Alexander Stoimenow |
Publisher | : CRC Press |
Total Pages | : 129 |
Release | : 2018-09-03 |
Genre | : Mathematics |
ISBN | : 1315359987 |
Download Diagram Genus, Generators, and Applications Book in PDF, ePub and Kindle
In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems. The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa’s algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps readers see applications of generators in a broader context.
Author | : Alexander Stoimenow |
Publisher | : |
Total Pages | : 18 |
Release | : 2006 |
Genre | : Braid theory |
ISBN | : |
Download Lie Groups, Burau Representation, and Non-conjugate Braids with the Same Closure Link Book in PDF, ePub and Kindle
Author | : Jane Gilman |
Publisher | : American Mathematical Soc. |
Total Pages | : 200 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821829661 |
Download Knots, Braids, and Mapping Class Groups -- Papers Dedicated to Joan S. Birman Book in PDF, ePub and Kindle
There are a number of specialties in low-dimensional topology that can find in their ``family tree'' a common ancestry in the theory of surface mappings. These include knot theory as studied through the use of braid representations, and 3-manifolds as studied through the use of Heegaard splittings. The study of the surface mapping class group (the modular group) is of course a rich subject in its own right, with relations to many different fields of mathematics and theoreticalphysics. However, its most direct and remarkable manifestation is probably in the vast area of low-dimensional topology. Although the scene of this area has been changed dramatically and experienced significant expansion since the original publication of Professor Joan Birman's seminal work,Braids, Links,and Mapping Class Groups(Princeton University Press), she brought together mathematicians whose research span many specialties, all of common lineage. The topics covered are quite diverse. Yet they reflect well the aim and spirit of the conference: to explore how these various specialties in low-dimensional topology have diverged in the past 20-25 years, as well as to explore common threads and potential future directions of development. This volume is dedicated to Joan Birman by hercolleagues with deep admiration and appreciation of her contribution to low-dimensional topology.
Author | : Vassily Olegovich Manturov |
Publisher | : CRC Press |
Total Pages | : 528 |
Release | : 2018-04-17 |
Genre | : Mathematics |
ISBN | : 1351359126 |
Download Knot Theory Book in PDF, ePub and Kindle
Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory’s state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.
Author | : Christian Kassel |
Publisher | : Springer Science & Business Media |
Total Pages | : 349 |
Release | : 2008-06-28 |
Genre | : Mathematics |
ISBN | : 0387685480 |
Download Braid Groups Book in PDF, ePub and Kindle
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.