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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 M3 be a closed hyperbolic three-manifold. We show that the number of genus g surface subgroups of π1(M3) grows like g2g.

Keywords
hyperbolic $3$–manifold, essential surface
Mathematical Subject Classification 2010
Primary: 57M50, 20H10
References
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