Spectral Flow for Dirac Operators with Magnetic Links
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- SPECTRAL FLOW OF DIRAC OPERATORS WITH
Accepted author manuscript, 611 KB, PDF document
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 the Euclidean three-space, the flux carried by an oriented knot features a 2 π-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 nontrivial. 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.
Original language | English |
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Journal | Journal of Geometric Analysis |
Volume | 30 |
Issue number | 1 |
Pages (from-to) | 1100-1167 |
ISSN | 1050-6926 |
DOIs | |
Publication status | Published - 2020 |
- Dirac operators, Knots, Links, Seifert surface, Spectral flow, Zero modes
Research areas
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