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Geometry-Topology Seminar

Thursday, February 15, 2018 - 4:45pm

Paul Melvin

Bryn Mawr College


University of Pennsylvania


Note that we are starting 15 minutes later than usual, at 4:45 instead of 4:30, so that Paul can get here after his class at Bryn Mawr.

It is known (by the work of Freedman, Perron and Quinn) that homologous surfaces of the same genus embedded with simply-connected complement in a smooth 4-manifold become smoothly isotopic aftersome number of stabilizations (connected summing the ambient 4-manifold with 2-sphere bundles over the 2-sphere).  Using Gabai's recent proof of the 4-dimensional light-bulb theorem, we show that a single stabilization always suffices.  Thus an alternative title for this talk is "One-is-enough".  This is joint work with Auckly, Kim, Ruberman and Schwartz.