Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Joint Spectral Flow and Localization of the Indices of Elliptic
  Operators   We introduce the notion of the joint spectral flow, which is a generalization
of the spectral flow, by using Segal's model of the connective $K$-theory
spectrum. We apply it for some localization results of indices motivated by
Witten's deformation of Dirac operators and rephrase some analytic techniques
in terms of topology.

28
The categories of this paper are: alg-geom
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The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph