Immersed surfaces in the modular orbifold

Details Immersed surfaces in the modular orbifold Immersed surfaces in the modular orbifold

2010-03-07

arxiv.org/abs/1003.1532v2

Proc. Amer. Math. Soc. 139 (2011), 2295-2308

Mathematics

Geometric Topology

13 pages, 8 figures; version 2 contains minor corrections

Scientific paper

A hyperbolic conjugacy class in the modular group PSL(2,Z) corresponds to a closed geodesic in the modular orbifold. Some of these geodesics virtually bound immersed surfaces, and some do not; the distinction is related to the polyhedral structure in the unit ball of the stable commutator length norm. We prove the following stability theorem: for every hyperbolic element of the modular group, the product of this element with a sufficiently large power of a parabolic element is represented by a geodesic that virtually bounds an immersed surface.

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