Floquet–Bloch Functions on Non-simply Connected Manifolds, the Aharonov–Bohm Fluxes, and Conformal Invariants of Immersed Surfaces

We define spectral (Bloch) varieties of multidimensional differential operators on non-simply connected manifolds. In their terms we give a description of the analytic dependence of the spectra of magnetic Laplacians on non-simply connected manifolds on the values of the Aharonov–Bohm fluxes, construct analogs of spectral curves for two-dimensional Dirac operators on Riemann surfaces, and thereby find new conformal invariants of immersions of surfaces into three- and four-dimensional Euclidean spaces.