2,307 research outputs found
The genus spectrum of a hyperbolic 3-manifold
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
We prove that any arithmetic hyperbolic -manifold of simplest type can
either be geodesically embedded into an arithmetic hyperbolic -manifold
or its universal 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
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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