Volume 3, issue 1 (1999)

Download this article
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The Burau representation is not faithful for $n = 5$

Stephen Bigelow

Geometry & Topology 3 (1999) 397–404

arXiv: math.GT/9904100

Abstract

The Burau representation is a natural action of the braid group Bn on the free [t,t1]–module of rank n 1. It is a longstanding open problem to determine for which values of n this representation is faithful. It is known to be faithful for n = 3. Moody has shown that it is not faithful for n 9 and Long and Paton improved on Moody’s techniques to bring this down to n 6. Their construction uses a simple closed curve on the 6–punctured disc with certain homological properties. In this paper we give such a curve on the 5–punctured disc, thus proving that the Burau representation is not faithful for n 5.

Keywords
braid group, Burau representation
Mathematical Subject Classification
Primary: 20F36
Secondary: 57M07, 20C99
References
Forward citations
Publication
Received: 21 July 1999
Accepted: 23 November 1999
Published: 30 November 1999
Proposed: Joan Birman
Seconded: Shigeyuki Morita, Dieter Kotschick
Authors
Stephen Bigelow
Department of Mathematics
University of California at Berkeley
Berkeley
California 94720
USA