#### Volume 16, issue 1 (2012)

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Counting essential surfaces in a closed hyperbolic three-manifold

### Jeremy Kahn and Vladimir Marković

Geometry & Topology 16 (2012) 601–624
##### Abstract

Let ${M}^{3}$ be a closed hyperbolic three-manifold. We show that the number of genus $g$ surface subgroups of ${\pi }_{1}\left({M}^{3}\right)$ grows like ${g}^{2g}$.

##### Keywords
hyperbolic $3$–manifold, essential surface
##### Mathematical Subject Classification 2010
Primary: 57M50, 20H10
##### Publication
Received: 5 January 2011
Revised: 26 October 2011
Accepted: 24 December 2011
Published: 8 April 2012
Proposed: David Gabai
Seconded: Tom Mrowka, Walter Neumann
##### Authors
 Jeremy Kahn Department of Mathematics Brown University Providence RI 02912 USA http://www.math.brown.edu/~kahn/ Vladimir Marković Department of Mathematics California Institute of Technology Pasadena CA 91105 USA http://www.its.caltech.edu/~markovic