Counting immersed surfaces in hyperbolic 3–manifolds

Masters, Joseph D

doi:10.2140/agt.2005.5.835

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Counting immersed surfaces in hyperbolic 3–manifolds

Joseph D Masters

Algebraic & Geometric Topology 5 (2005) 835–864

DOI: 10.2140/agt.2005.5.835

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

Volume 5, issue 2 (2005)