Communications in Analysis and Geometry

Volume 23 (2015)

Number 2

Surfaces that become isotopic after Dehn filling

Pages: 363 – 376



David Bachman (Pitzer College, Claremont, California, U.S.A.)

Ryan Derby-Talbot (Quest University, Squamish, British Columbia, Canada)

Eric Sedgwick (College of Computing and Digital Media, DePaul University, Chicago, Illinois, U.S.A.)


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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Published 17 December 2014