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arXiv · 1701.02130

On the bottom of spectra under coverings

Werner Ballmann·Henrik Matthiesen·Panagiotis Polymerakis
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Abstract

For a Riemannian covering $M_1\to M_0$ of complete Riemannian manifolds with boundary (possibly empty) and respective fundamental groups $\Gamma_1\subseteq\Gamma_0$, we show that the bottoms of the spectra of $M_0$ and $M_1$ coincide if the right action of $\Gamma_0$ on $\Gamma_1\backslash\Gamma_0$ is amenable.

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Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis. 2017-01-09. On the bottom of spectra under coverings. https://arxiv.org/abs/1701.02130

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