Geometry & Topology

Counting essential surfaces in a closed hyperbolic three-manifold

Jeremy Kahn and Vladimir Marković

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

Article information

Geom. Topol., Volume 16, Number 1 (2012), 601-624.

Received: 5 January 2011
Revised: 26 October 2011
Accepted: 24 December 2011
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]

hyperbolic $3$–manifold essential surface


Kahn, Jeremy; Marković, Vladimir. Counting essential surfaces in a closed hyperbolic three-manifold. Geom. Topol. 16 (2012), no. 1, 601--624. doi:10.2140/gt.2012.16.601.

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