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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Immersed surfaces in the modular orbifold


Authors: Danny Calegari and Joel Louwsma
Journal: Proc. Amer. Math. Soc. 139 (2011), 2295-2308
MSC (2010): Primary 20F65, 20H10, 57M07
Published electronically: March 7, 2011
MathSciNet review: 2784794
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Abstract: A hyperbolic conjugacy class in the modular group $ \mathrm{PSL}(2,\mathbb{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

Danny Calegari
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: dannyc@its.caltech.edu

Joel Louwsma
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: louwsma@caltech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10911-0
PII: S 0002-9939(2011)10911-0
Received by editor(s): April 19, 2010
Published electronically: March 7, 2011
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.