Algebraic & Geometric Topology

Counting immersed surfaces in hyperbolic 3–manifolds

Joseph D Masters

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We count the number of conjugacy classes of maximal, genus g, surface subroups in hyperbolic 3–manifold groups. For any closed hyperbolic 3–manifold, we show that there is an upper bound on this number which grows factorially with g. We also give a class of closed hyperbolic 3–manifolds for which there is a lower bound of the same type.

Article information

Algebr. Geom. Topol., Volume 5, Number 2 (2005), 835-864.

Received: 20 October 2004
Accepted: 13 June 2005
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
Secondary: 57N16: Geometric structures on manifolds [See also 57M50] 57M27: Invariants of knots and 3-manifolds

surface subgroups bending pleated surfaces reflection orbifolds


Masters, Joseph D. Counting immersed surfaces in hyperbolic 3–manifolds. Algebr. Geom. Topol. 5 (2005), no. 2, 835--864. doi:10.2140/agt.2005.5.835.

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