E-Book, Englisch, 237 Seiten
Birman Braids, Links, and Mapping Class Groups
1. Auflage 2016
ISBN: 978-1-4008-8142-0
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, 237 Seiten
Reihe: Annals of Mathematics Studies
ISBN: 978-1-4008-8142-0
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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.
Autoren/Hrsg.
Weitere Infos & Material
Frontmatter, pg. i
PREFACE, pg. v
TABLE OF CONTENTS, pg. ix
CHAPTER 1. BRAID GROUPS, pg. 1
CHAPTER 2. BRAIDS AND LINKS, pg. 37
CHAPTER 3. MAGNUS REPRESENTATIONS, pg. 102
CHAPTER 4. MAPPING CLASS GROUPS, pg. 148
CHAPTER 5. PLATS AND LINKS, pg. 192
APPENDIX: RESEARCH PROBLEMS, pg. 216
BIBLIOGRAPHY, pg. 221
INDEX, pg. 227
Backmatter, pg. 229
