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The
center of some braid groups and the Farrell cohomology of
certain pure mapping class groups
Yu Qing Chen, Henry H Glover and Craig A Jensen |
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Algebraic & Geometric Topology 7 (2007) 1987–2006
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arXiv: 0712.3334 |
Abstract |
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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 –primary part of the Farrell cohomology groups of certain mapping class groups are elementary abelian groups. At the end we compute the –primary part of the Farrell cohomology of a few pure mapping class groups. |
Keywords
braid group, mapping class group, normalizer, centralizer,
cohomology of groups
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Mathematical Subject Classification 2000
Primary: 20F36, 20J06
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References |
Publication
Received: 14 March 2007
Revised: 16 September 2007
Accepted: 5 October 2007
Published: 26 December 2007
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Authors |
| Yu Qing Chen | |
| Department of Mathematics and
Statistics Wright State University Dayton OH 45435-0001 |
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| Henry H Glover | |
| Department of Mathematics Ohio State University Columbus OH 43210-1174 |
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| Craig A Jensen | |
| Department of Mathematics University of New Orleans New Orleans LA 70148 |
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