Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher analytic torsion and cohomology of diffeomorphism groups   We consider a closed odd-dimensional oriented manifold $M$ together with an
acyclic flat hermitean vector bundle $\cF$. We form the trivial fibre bundle
with fibre $M$ over the manifold of all Riemannian metrics on $M$. It has a
natural flat connection and a vertical Riemannian metric. The higher analytic
torsion form of Bismut/Lott associated to the situation is invariant with
respect to the connected component of the identity of the diffeomorphism group
of $M$. Using that the space of Riemannian metrics is contractible we define
continuous cohomology classes of the diffeomorphism group and its Lie algebra.
For the circle we compute this classes in degree 2 and show that the group
cohomology class is non-trivial, while the Lie algebra cohomology class
vanishes.

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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn