Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cyclic Homology and Group Actions   In this paper we present the construction of explicit quasi-isomorphisms that
compute the cyclic homology and periodic cyclic homology of crossed-product
algebras associated with (discrete) group actions. In the first part we deal
with algebraic crossed-products associated with group actions on unital
algebras over any ring $k\supset \mathbb{Q}$. In the second part, we extend the
results to actions on locally convex algebras. We then deal with
crossed-products associated with group actions on manifolds and smooth
varieties. For the finite order components, the results are expressed in terms
of what we call "mixed equivariant cohomology". This "mixed" theory mediates
between group homology and de Rham cohomology. It is naturally related to
equivariant cohomology, and so we obtain explicit constructions of cyclic
cycles out of equivariant characteristic classes. For the infinite order
components, we simplify and correct the misidentification of Crainic. An
important new homological tool is the notion of "triangular $S$-module". This
is a natural generalization of the cylindrical complexes of Getzler-Jones. It
combines the mixed complexes of Burghelea-Kassel and parachain complexes of
Getzler-Jones with the $S$-modules of Kassel-Jones. There are spectral
sequences naturally associated with triangular $S$-modules. In particular, this
allows us to recover spectral sequences Feigin-Tsygan and Getzler-Jones and
leads us to a new spectral sequence.

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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph