Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A classifying space for commutativity in Lie groups   In this article we consider a space B_{com}G assembled from commuting
elements in a Lie group G first defined in [Adem, Cohen, Torres-Giese 2012]. We
describe homotopy-theoretic properties of these spaces using homotopy colimits,
and their role as a classifying space for transitionally commutative bundles.
We prove that ZxB_{com}U is a loop space and define a notion of commutative
K-theory for bundles over a finite complex X which is isomorphic to
[X,ZxB_{com}U]. We compute the rational cohomology of B_{com}G for G equal to
any of the classical groups U(n), SU(n) and Sp(n), and exhibit the rational
cohomologies of B_{com}U, B_{com}SU and B_{com}Sp as explicit polynomial rings.

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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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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: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: eess