Volume 15, issue 4 (2015)

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Stable immersions in orbifolds

Alden Walker

Algebraic & Geometric Topology 15 (2015) 1877–1908

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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immersion, orbifold, scl, stable commutator length
Mathematical Subject Classification 2010
Primary: 20F65, 57M07
Secondary: 57R42, 57R18
Received: 7 January 2014
Revised: 20 November 2014
Accepted: 23 November 2014
Published: 10 September 2015
Alden Walker
Department of Mathematics
University of Chicago
5734 S University Avenue
Chicago, IL 60637