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Upper bounds on the topological four-ball genus using classical knot invariants


Speaker: Peter Feller, Boston Univ
Location: 2112 MSB
Start time: Tue, May 17 2016, 1:10PM

As a knot theoretic consequence of Freedman's spectacular disc theorem, it is know that knots with Alexander polynomial 1 are topologically slice---they are the boundary of a locally flat embedding of the 2-disc into the 4-ball. Based on this, we provide upper bounds on the topological 4-ball genus of knots in terms of their Seifert form. As a consequence, we show that the smooth and the topological 4-ball genus differ on simple classes of knots such as torus knots and two-bridge knots. The latter translates to interesting differences between smooth and topological 4-manifolds.

This talk is partially based on work with Duncan McCoy and work with Sebastian Baader, Lukas Lewark, and Livio Liechti."