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)


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


Zbl 0810.57011
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