Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hopf cyclic cohomology and Hodge theory for proper actions   We introduce a Hopf algebroid associated to a proper Lie group action on a
smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is
equal to the de Rham cohomology of invariant differential forms. When the
action is cocompact, we develop a generalized Hodge theory for the de Rham
cohomology of invariant differential forms. We prove that every cyclic
cohomology class of the Hopf algebroid is represented by a generalized harmonic
form. This implies that the space of cyclic cohomology of the Hopf algebroid is
finite dimensional. As an application of the techniques developed in this
paper, we discuss properties of the Euler characteristic for a proper cocompact
action.

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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex