Canary, Richard D. Ends of hyperbolic 3-manifolds. (English) Zbl 0810.57006 J. Am. Math. Soc. 6, No. 1, 1-35 (1993). 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) Cited in 4 ReviewsCited in 61 Documents 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 Keywords:complete, hyperbolic 3-manifold; topologically tame; homeomorphic to the interior of a compact 3-manifold; geometrically tame; ends Citations:Zbl 0810.57011 PDFBibTeX XMLCite \textit{R. D. Canary}, J. Am. Math. Soc. 6, No. 1, 1--35 (1993; Zbl 0810.57006) Full Text: DOI