Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology of groups in o-minimal structures: acyclicity of the
  infinitesimal subgroup   By recent work on some conjectures of Pillay, each definably compact group in
a saturated o-minimal structure is an expansion of a compact Lie group by a
torsion free normal divisible subgroup, called its infinitesimal subgroup. We
show that the infinitesimal subgroup is cohomologically acyclic. This implies
that the functorial correspondence between definably compact groups and Lie
groups preserves the cohomology.

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The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga