Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Proof of Tsygan's Formality Conjecture for an Arbitrary Smooth
  Manifold   Proofs of Tsygan's formality conjectures for chains would unlock important
algebraic tools which might lead to new generalizations of the
Atiyah-Patodi-Singer index theorem and the Riemann-Roch-Hirzebruch theorem.
Despite this pivotal role in the traditional investigations and the efforts of
various people the most general version of Tsygan's formality conjecture has
not yet been proven. In my thesis I propose Fedosov resolutions for the
Hochschild cohomological and homological complexes of the algebra of functions
on an arbitrary smooth manifold. Using these resolutions together with
Kontsevich's formality quasi-isomorphism for Hochschild cochains of R[[y_1,
>..., y_d]] and Shoikhet's formality quasi-isomorphism for Hochschild chains of
R[[y_1,..., y_d]] I prove Tsygan's formality conjecture for Hochschild chains
of the algebra of functions on an arbitrary smooth manifold. The construction
of the formality quasi-isomorphism for Hochschild chains is manifestly
functorial for isomorphisms of the pairs (M,\nabla), where M is the manifold
and \nabla is an affine connection on the tangent bundle. In my thesis I apply
these results to equivariant quantization, computation of Hochschild homology
of quantum algebras and description of traces in deformation quantization.

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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: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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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: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int