2,306 research outputs found

    The genus spectrum of a hyperbolic 3-manifold

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    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

    Embedding arithmetic hyperbolic manifolds

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    We prove that any arithmetic hyperbolic nn-manifold of simplest type can either be geodesically embedded into an arithmetic hyperbolic (n+1)(n+1)-manifold or its universal mod 2\mathrm{mod}~2 Abelian cover can.Comment: 20 pages; revised version, typos corrected; Mathematical Research Letters vol. 25, no.

    The Bianchi groups are subgroup separable on geometrically finite subgroups

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    We show that for certain arithmetic groups, geometrically finite subgroups are the intersection of finite index subgroups containing them. Examples are the Bianchi groups and the Seifert-Weber dodecahedral space. In particular, for manifolds commensurable with these groups, immersed incompressible surfaces lift to embeddings in a finite sheeted covering.Comment: 19 page
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