Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differentiable cyclic cohomology and Hopf algebraic structures in
  transverse geometry   We prove a cyclic cohomological analogue of Haefliger's van Est-type theorem
for the groupoid of germs of diffeomorphisms of a manifold. The differentiable
version of cyclic cohomology is associated to the algebra of transverse
differential operators on that groupoid, which is shown to carry an intrinsic
Hopf algebraic structure. We establish a canonical isomorphism between the
periodic Hopf cyclic cohomology of this extended Hopf algebra and the
Gelfand-Fuchs cohomology of the Lie algebra of formal vector fields. We then
show that this isomorphism can be explicitly implemented at the cochain level,
by a cochain map constructed out of a fixed torsion-free linear connection.
This allows the direct treatment of the index formula for the hypoelliptic
signature operator - representing the diffeomorphism invariant transverse
fundamental $K$-homology class of an oriented manifold - in the general case,
when this operator is constructed by means of an arbitrary coupling connection.

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The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys