Algebraic & Geometric Topology

The center of some braid groups and the Farrell cohomology of certain pure mapping class groups

Yu Qing Chen, Henry Glover, and Craig Jensen

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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.

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 4 (2007), 1987-2006.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796780

Digital Object Identifier
doi:10.2140/agt.2007.7.1987

Mathematical Reviews number (MathSciNet)
MR2366185

Zentralblatt MATH identifier
1161.20033

Subjects
Primary: 20F36: Braid groups; Artin groups 20J06: Cohomology of groups

Keywords
braid group mapping class group normalizer centralizer cohomology of groups

Citation

Chen, Yu Qing; Glover, Henry; Jensen, Craig. The center of some braid groups and the Farrell cohomology of certain pure mapping class groups. Algebr. Geom. Topol. 7 (2007), no. 4, 1987--2006. doi:10.2140/agt.2007.7.1987. https://projecteuclid.org/euclid.agt/1513796780


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References

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