Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polyhedral Gauss-Bonnet theorems and valuations   The Gauss-Bonnet theorem for a polyhedron (a union of finitely many compact
convex polytopes) in $n$-dimensional Euclidean space expresses the Euler
characteristic of the polyhedron as a sum of certain curvatures, which are
different from zero only at the vertices of the polyhedron. This note suggests
a generalization of these polyhedral vertex curvatures, based on valuations,
and thus obtains a variety of polyhedral Gauss-Bonnet theorems.

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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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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: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci