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2001 The mapping class group of a genus two surface is linear
Stephen Bigelow, Ryan Budney
Algebr. Geom. Topol. 1(2): 699-708 (2001). DOI: 10.2140/agt.2001.1.699

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.

Citation

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Stephen Bigelow. Ryan Budney. "The mapping class group of a genus two surface is linear." Algebr. Geom. Topol. 1 (2) 699 - 708, 2001. https://doi.org/10.2140/agt.2001.1.699

Information

Received: 2 August 2001; Revised: 15 November 2001; Accepted: 16 November 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 0999.57020
MathSciNet: MR1875613
Digital Object Identifier: 10.2140/agt.2001.1.699

Subjects:
Primary: 20F36
Secondary: 20C15, 57M07

Rights: Copyright © 2001 Mathematical Sciences Publishers

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