Surfaces that become isotopic after Dehn filling

Details Surfaces that become isotopic after Dehn filling Surfaces that become isotopic after Dehn filling

2010-01-24

arxiv.org/abs/1001.4259v1

Mathematics

Geometric Topology

14 pages, 5 figures

Scientific paper

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.

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