Geometry & Topology 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

DOI: 10.2140/gt.2012.16.601

Abstract

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

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