Stable immersions in orbifolds

We prove that in any hyperbolic orbifold with one boundary component, the product of any hyperbolic fundamental group element with a sufficiently large multiple of the boundary is represented by a geodesic loop that virtually bounds an immersed surface. In the case that the orbifold is a disk, there are some conditions. Our results generalize work of Calegari–Louwsma and resolve a conjecture of Calegari.

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Keywords

immersion, orbifold, scl, stable commutator length

Mathematical Subject Classification 2010

Primary: 20F65, 57M07

Secondary: 57R42, 57R18

References

Publication

Received: 7 January 2014

Revised: 20 November 2014

Accepted: 23 November 2014

Published: 10 September 2015

Authors

Alden Walker
Department of Mathematics University of Chicago 5734 S University Avenue Chicago, IL 60637 USA
http://math.uchicago.edu/~akwalker

Volume 15, issue 4 (2015)

Alden Walker

Abstract