The spectrum of a solenoid

Raymond Lei

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arXiv · 1907.06712

The spectrum of a solenoid

Raymond Lei

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Abstract

Given a sequence of regular finite coverings of complete 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.

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Raymond Lei. 2019-11-20. The spectrum of a solenoid. https://arxiv.org/abs/1907.06712

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