Counting immersed surfaces in hyperbolic 3-manifolds

Details Counting immersed surfaces in hyperbolic 3-manifolds Counting immersed surfaces in hyperbolic 3-manifolds

2002-05-23

arxiv.org/abs/math/0205250v4

Algebr. Geom. Topol. 5 (2005) 835-864

Mathematics

Geometric Topology

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

Scientific paper

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.

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