#### 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