Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Index pairings in presence of symmetries with applications to
  topological insulators   In a basic framework of a complex Hilbert space equipped with a complex
conjugation and an involution, linear operators can be real, quaternionic,
symmetric or anti-symmetric, and orthogonal projections can furthermore be
symplectic. This paper investigates index pairings of projections and unitaries
submitted to such symmetries. Various scenarios emerge: Noether indices can
take either arbitrary integer values or only even integer values or they can
vanish and then possibly have secondary $\mathbb{Z}_2$-invariants. These
general results are applied to prove index theorems for the strong invariants
of topological insulators. The symmetries come from the Fermi projection
($K$-theoretic part of the pairing) and the Dirac operator ($K$-homological
part of the pairing depending on the dimension of physical space).

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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
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The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an