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arXiv · 2403.11161

Floquet-Bloch functions on non-simply connected manifolds, the Aharonov-Bohm fluxes, and conformal invariants of immersed surfaces

I. A. Taimanov
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Abstract

Spectral (Bloch) varieties of multidimensional differential operators on non-simply connected manifolds are defined. In their terms it is given a description of the analytical dependence of the spectra of magnetic Laplacians on non-simply connected manifolds on the values of the Aharonov-Bohm fluxes and a construction of analogues of spectral curves for two-dimensional Dirac operators on Riemann surfaces and, thereby, new conformal invariants of immersions of surfaces into 3- and 4-dimensional Euclidean spaces.

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BibTeXRIS

I. A. Taimanov. 2024-03-17. Floquet-Bloch functions on non-simply connected manifolds, the Aharonov-Bohm fluxes, and conformal invariants of immersed surfaces. https://arxiv.org/abs/2403.11161

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