We count the number of conjugacy classes of maximal, genus , 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 . We also give a class of closed hyperbolic 3–manifolds for which there is a lower bound of the same type.
"Counting immersed surfaces in hyperbolic 3–manifolds." Algebr. Geom. Topol. 5 (2) 835 - 864, 2005. https://doi.org/10.2140/agt.2005.5.835