Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The center of some braid groups and the Farrell cohomology of certain
  pure mapping class groups   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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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex