Volume 1, issue 2 (2001)

Download this article
For printing
Recent Issues

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
The mapping class group of a genus two surface is linear

Stephen Bigelow and Ryan D Budney

Algebraic & Geometric Topology 1 (2001) 699–708

arXiv: math.GT/0010310

Abstract

In this paper we construct a faithful representation of the mapping class group of the genus two surface into a group of matrices over the complex numbers. Our starting point is the Lawrence–Krammer representation of the braid group Bn, which was shown to be faithful by Bigelow and Krammer. We obtain a faithful representation of the mapping class group of the n–punctured sphere by using the close relationship between this group and Bn1. We then extend this to a faithful representation of the mapping class group of the genus two surface, using Birman and Hilden’s result that this group is a 2 central extension of the mapping class group of the 6–punctured sphere. The resulting representation has dimension sixty-four and will be described explicitly. In closing we will remark on subgroups of mapping class groups which can be shown to be linear using similar techniques.

Keywords
mapping class group, braid group, linear, representation
Mathematical Subject Classification 2000
Primary: 20F36
Secondary: 57M07, 20C15
References
Forward citations
Publication
Received: 2 August 2001
Revised: 15 November 2001
Accepted: 16 November 2001
Published: 22 November 2001
Authors
Stephen Bigelow
Department of Mathematics and Statistics
University of Melbourne
Parkville
Victoria, 3010
Australia
Ryan D Budney
Department of Mathematics
Cornell University
Ithaca NY 14853-4201
USA