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Immersed surfaces in the modular orbifold

Calegari, Danny and Louwsma, Joel (2011) Immersed surfaces in the modular orbifold. Proceedings of the American Mathematical Society, 139 (7). pp. 2295-2308. ISSN 0002-9939.

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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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Additional Information:© 2011 American Mathematical Society. Reverts to public domain 28 years from publication. Communicated by Alexander N. Dranishnikov. Article electronically published on March 7, 2011. The first author was supported by NSF grant DMS 0707130. We would like to thank Benson Farb and Eric Rains for some useful conversations regarding this material.
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NSFDMS 0707130
Issue or Number:7
Record Number:CaltechAUTHORS:20110805-111542579
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24708
Deposited By: Tony Diaz
Deposited On:26 Oct 2011 21:25
Last Modified:03 Oct 2019 02:59

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