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Ends of hyperbolic 3-manifolds. (English) Zbl 0810.57006
The main result of this paper is that a complete, hyperbolic 3-manifold $$N$$ which is topologically tame in the sense that $$N$$ is homeomorphic to the interior of a compact 3-manifold with boundary is geometrically tame – the ends of $$N$$ are either geometrically finite or simply degenerate. The structure of geometrically tame hyperbolic 3-manifolds is quite well understood; it is still an open question as to whether a complete, hyperbolic 3-manifold with finitely generated fundamental group is necessarily topologically tame.
Reviewer: J.Hempel (Houston)

##### MSC:
 57M50 General geometric structures on low-dimensional manifolds 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) 57N10 Topology of general $$3$$-manifolds (MSC2010) 58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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