Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hopf Index Theorem for foliations   We formulate and prove an analog of the Hopf Index Theorem for Riemannian
foliations. We compute the basic Euler characteristic of a closed Riemannian
manifold as a sum of indices of a non-degenerate basic vector field at critical
leaf closures. The primary tool used to establish this result is an adaptation
to foliations of the Witten deformation method.

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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an