Braids Links And Mapping Class Groups
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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.
Braids Links And Mapping Class Groups
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Author : Joan S. Birman
language : en
Publisher: Princeton University Press
Release Date : 1974
Braids Links And Mapping Class Groups 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 1974 with Crafts & Hobbies 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.
Braids Links And Mapping Class Groups Based On Lecture Notes By James Cannon
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Author :
language : en
Publisher:
Release Date : 1975
Braids Links And Mapping Class Groups Based On Lecture Notes By James Cannon written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Knots Braids And Mapping Class Groups Papers Dedicated To Joan S Birman
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Author : Jane Gilman
language : en
Publisher: American Mathematical Soc.
Release Date :
Knots Braids And Mapping Class Groups Papers Dedicated To Joan S Birman written by Jane Gilman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Knots Braids And Mapping Class Groups Papers Dedicated To Joan S Birman
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Author : Jane Gilman
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Knots Braids And Mapping Class Groups Papers Dedicated To Joan S Birman written by Jane Gilman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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.
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.
Braids
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Author : Joan S. Birman
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Braids written by Joan S. Birman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group, held at the University of California, Santa Cruz, in July 1986. This work is suitable for graduate students and researchers who wish to learn more about braids, as well as more experienced workers in this area.
Problems On Mapping Class Groups And Related Topics
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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-09-12
Problems On Mapping Class Groups And Related Topics written by Benson Farb and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-12 with Mathematics categories.
The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
Braid Groups And Their Relationship To Mapping Class Groups
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Author : Joan S. Birman
language : en
Publisher:
Release Date : 1968
Braid Groups And Their Relationship To Mapping Class Groups written by Joan S. Birman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Braids And Mapping Class Groups
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Author : John Scott Maginnis
language : en
Publisher:
Release Date : 1987
Braids And Mapping Class Groups written by John Scott Maginnis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.