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2007 The center of some braid groups and the Farrell cohomology of certain pure mapping class groups
Yu Qing Chen, Henry Glover, Craig Jensen
Algebr. Geom. Topol. 7(4): 1987-2006 (2007). DOI: 10.2140/agt.2007.7.1987

Abstract

In this paper we first show that many braid groups of low genus surfaces have their centers as direct factors. We then give a description of centralizers and normalizers of prime order elements in pure mapping class groups of surfaces with spherical quotients using automorphism groups of fundamental groups of the quotient surfaces. As an application, we use these to show that the p–primary part of the Farrell cohomology groups of certain mapping class groups are elementary abelian groups. At the end we compute the p–primary part of the Farrell cohomology of a few pure mapping class groups.

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Yu Qing Chen. Henry Glover. Craig Jensen. "The center of some braid groups and the Farrell cohomology of certain pure mapping class groups." Algebr. Geom. Topol. 7 (4) 1987 - 2006, 2007. https://doi.org/10.2140/agt.2007.7.1987

Information

Received: 14 March 2007; Revised: 16 September 2007; Accepted: 5 October 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1161.20033
MathSciNet: MR2366185
Digital Object Identifier: 10.2140/agt.2007.7.1987

Subjects:
Primary: 20F36, 20J06

Rights: Copyright © 2007 Mathematical Sciences Publishers

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Vol.7 • No. 4 • 2007
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