Volume 5, issue 2 (2005)

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Counting immersed surfaces in hyperbolic 3–manifolds

Joseph D Masters

Algebraic & Geometric Topology 5 (2005) 835–864

arXiv: math.GT/0205250

Abstract

We count the number of conjugacy classes of maximal, genus g, surface subroups in hyperbolic 3–manifold groups. For any closed hyperbolic 3–manifold, we show that there is an upper bound on this number which grows factorially with g. We also give a class of closed hyperbolic 3–manifolds for which there is a lower bound of the same type.

Keywords
surface subgroups, bending, pleated surfaces, reflection orbifolds
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 57N16, 57M27
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Publication
Received: 20 October 2004
Accepted: 13 June 2005
Published: 24 July 2005
Authors
Joseph D Masters
Mathematics Department
Rice University
Houston TX 77005
USA
Mathematics Department
SUNY Buffalo
Buffalo NY 14260
USA