Algebraic and Geometric Topology 5 (2005), paper no. 35, pages 835-864.

Counting immersed surfaces in hyperbolic 3-manifolds

Joseph D. Masters

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

AMS subject classification. Primary: 57M50. Secondary: 57N16, 57M27.

E-print: arXiv:math.GT/0205250

DOI: 10.2140/agt.2005.5.835

Submitted: 20 October 2004. Accepted: 13 June 2005. Published: 24 July 2005.

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Joseph D. Masters
Mathematics Department, Rice University, Houston TX 77005, USA
Current address:
Mathematics Department, SUNY Buffalo, Buffalo NY 14260, USA
Email: mastersj@rice.edu, jdmaster@buffalo.edu

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