Braids, links, and mapping class groups. Annals of mathematics studies 82.

Birman, Joan S.:

ISBN 10: 0691081492 / ISBN 13: 9780691081496

Published by Princeton, Princeton University Press, 1974

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 55 BIR 9780691081496 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2509033

Bibliographic Details

• Title: Braids, links, and mapping class groups. Annals of mathematics studies 82.
• Publisher: Princeton, Princeton University Press
• Publication Date: 1974
• Language: English
• ISBN 10: 0691081492
• ISBN 13: 9780691081496
• Binding: Hardcover
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

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.