Bowditch, B. H. (Brian Hayward), 1961- . (2010) Notes on tameness. L' Enseignement Mathematique, Vol.56 . pp. 229-285. ISSN 0013-8584

Abstract

It has been shown by Bonahon, Agol, Calegari and Gabai that a complete hyperbolic 3-manifold with finitely generated fundamental group is topologically finite. This was conjectured by Marden, and via a geometric reinterpretation by Thurston, has become known as the ``Tameness Theorem''. In this paper we give an account of this result, inspired by arguments of Soma, which is as far as possible self-contained. We also describe how it can be generalised to pinched negative curvature, and how it implies a version of Ahlfors's finiteness theorem in this context.

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