Surfaces that become isotopic after Dehn filling
Geometric Topology
2013-02-28 v2
Abstract
We show that after generic filling along a torus boundary component of a 3-manifold, no two closed, 2-sided, essential surfaces become isotopic, and no closed, 2-sided, essential surface becomes inessential. That is, the set of essential surfaces (considered up to isotopy) survives unchanged in all suitably generic Dehn fillings. Furthermore, for all but finitely many non-generic fillings, we show that two essential surfaces can only become isotopic in a constrained way.
Cite
@article{arxiv.1001.4259,
title = {Surfaces that become isotopic after Dehn filling},
author = {David Bachman and Ryan Derby-Talbot and Eric Sedgwick},
journal= {arXiv preprint arXiv:1001.4259},
year = {2013}
}
Comments
Revised version, incorporates updated references and improved exposition