Geometry & Topology

Counting essential surfaces in a closed hyperbolic three-manifold

Jeremy Kahn and Vladimir Marković

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732390

Digital Object Identifier
doi:10.2140/gt.2012.16.601

Mathematical Reviews number (MathSciNet)
MR2916295

Zentralblatt MATH identifier
1283.57021

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

Keywords
hyperbolic $3$–manifold essential surface

Citation

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. https://projecteuclid.org/euclid.gt/1513732390


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