Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: O-minimal spectra, infinitesimal subgroups and cohomology   By recent work on some conjectures of Pillay, each definably compact group
$G$ in a saturated o-minimal expansion of an ordered field has a normal
``infinitesimal subgroup'' $G^{00}$ such that the quotient $G/G^{00}$, equipped
with the ``logic topology'', is a compact (real) Lie group. Our first result is
that the functor $G\mapsto G/G^{00}$ sends exact sequences of definably compact
groups into exacts sequences of Lie groups. We then study the connections
between the Lie group $G/G^{00}$ and the o-minimal spectrum $\widetilde G$ of
$G$. We prove that $G/G^{00}$ is a topological quotient of $\widetilde G$. We
thus obtain a natural homomorphism $\Psi^*$ from the cohomology of $G/G^{00}$
to the (\v{C}ech-)cohomology of $\widetilde G$. We show that if $G^{00}$
satisfies a suitable contractibility conjecture then $\widetilde {G^{00}}$ is
acyclic in \v{C}ech cohomology and $\Psi^*$ is an isomorphism. Finally we prove
the conjecture in some special cases.

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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin