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Given a sequence of regular finite coverings of Riemannian manifolds, we consider the covering solenoid associated with the sequence. We study the leaf-wise Laplacian on the covering solenoid. The main result is that the spectrum of the Laplacian on the covering solenoid equals the closure of the union of the spectra of the manifolds in the sequence. We offer an equivalent statement of Selberg's 1/4 conjecture.
Furthermore, we discuss the spectrum of a solenoid in special cases such as a tower of toruses and a tower of hyperbolic surfaces by applying established results for a tower of coverings. We talk about the geodesic flow on a solenoid.
| Advisor: | Judge, Christopher |
| Commitee: | Connell, Chris, Pilgrim, Kevin, Thurston, Dylan |
| School: | Indiana University |
| Department: | Mathematics |
| School Location: | United States -- Indiana |
| Source: | DAI-B 81/12(E), Dissertation Abstracts International |
| Source Type: | DISSERTATION |
| Subjects: | Mathematics |
| Keywords: | Solenoid, Spectrum |
| Publication Number: | 28000771 |
| ISBN: | 9798661918192 |
