SPECTRA OF Sol-MANIFOLDS: ARITHMETIC AND QUANTUM MONODROMY
نویسنده
چکیده
The spectral problem of the three-dimensional manifolds M3 A admitting Sol-geometry in Thurston’s sense is investigated. Topologically M3 A are the torus bundles over a circle with a hyperbolic glueing map A. The eigenfunctions of the corresponding Laplace-Beltrami operators are described in terms of the modified Mathieu functions. It is shown that the multiplicities of the eigenvalues do not depend on the parameters in the metric and are directly related to the number of representations of an integer by a given indefinite binary quadratic form. The quantum monodromy phenomenon for the corresponding quantum system is discussed.
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