Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral flow for Dirac operators with magnetic links   This paper is devoted to the study of the spectral properties of Dirac
operators on the three-sphere with singular magnetic fields supported on
smooth, oriented links. As for Aharonov-Bohm solenoids in Euclidean
three-space, the flux carried by an oriented knot features a $2\pi$-periodicity
of the associated operator. For a given link one thus obtains a family of Dirac
operators indexed by a torus of fluxes. We study the spectral flow of paths of
such operators corresponding to loops in this torus. The spectral flow is in
general non-trivial. In the special case of a link of unknots we derive an
explicit formula for the spectral flow of any loop on the torus of fluxes. It
is given in terms of the linking numbers of the knots and their writhes.

31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys