Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A renormalized index theorem for some complete asymptotically regular
  metrics: the Gauss-Bonnet theorem   The Gauss-Bonnet Theorem is studied for edge metrics as a renormalized index
theorem. These metrics include the Poincar\'e-Einstein metrics of the AdS/CFT
correspondence. Renormalization is used to make sense of the curvature integral
and the dimensions of the $L^2$-cohomology spaces as well as to carry out the
heat equation proof of the index theorem. For conformally compact metrics even
mod $x^m$, the finite time supertrace of the heat kernel on conformally compact
manifolds is shown to renormalize independently of the choice of special
boundary defining function.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
19
The categories of this paper are: eess