Immersed surfaces in the modular orbifold
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- by Danny Calegari and Joel Louwsma PDF
- Proc. Amer. Math. Soc. 139 (2011), 2295-2308 Request permission
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.References
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Additional Information
- Danny Calegari
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 605373
- Email: dannyc@its.caltech.edu
- Joel Louwsma
- Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- Email: louwsma@caltech.edu
- Received by editor(s): April 19, 2010
- Published electronically: March 7, 2011
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2295-2308
- MSC (2010): Primary 20F65, 20H10, 57M07
- DOI: https://doi.org/10.1090/S0002-9939-2011-10911-0
- MathSciNet review: 2784794