Counting immersed surfaces in hyperbolic 3-manifolds

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.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-35.abs.html

Cited by in corpus (4)

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• Kleinian groups with ubiquitous surface subgroups
• Determining hyperbolic 3-manifolds by their surfaces