The genus spectrum of a hyperbolic 3-manifold

D. B. McReynolds; Alan W. Reid

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arXiv · 0901.4086

The genus spectrum of a hyperbolic 3-manifold

D. B. McReynolds·Alan W. Reid

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Abstract

In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic surface, this spectrum determines the commensurability class. In addition, we show that any finite volume hyperbolic 3-manifold has many pairs of non-isometric finite covers with identical spectra. Forgetting multiplicities, we can also construct pairs where the volume ratio is unbounded.

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D. B. McReynolds, Alan W. Reid. 2009-01-26. The genus spectrum of a hyperbolic 3-manifold. https://arxiv.org/abs/0901.4086

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