Stable immersions in orbifolds
arXiv:1312.2862 · doi:10.2140/agt.2015.15.1877
Abstract
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.
Better proofs; better pictures. (27 pages, 21 figures)