Algebraic & Geometric Topology 7 (2007) 1987–2006

DOI: 10.2140/agt.2007.7.1987

arXiv: 0712.3334

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.

Keywords

braid group, mapping class group, normalizer, centralizer, cohomology of groups

Mathematical Subject Classification

Primary: 20F36, 20J06

References

Publication

Received: 14 March 2007
Revised: 16 September 2007
Accepted: 5 October 2007
Published: 26 December 2007

Authors