Seifert pairing bounds on the topological slice genus of knots

Seifert pairing bounds on the topological slice genus of knots

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Peter Feller , Boston College
Fine Hall 314

We present upper bounds for the topological slice genus of knots coming from the Seifert pairing. The main ingredient in the proof is 3-dimensional reduction to a consequence of Freedman's disk theorem: knots with trivial Alexander polynomial are topologically slice. These bounds yield surprising consequences for simple families of knots such as torus knots and 2-bridge knots that contrast smooth results coming from the Thom conjecture and Donaldson's diagonalization theorem. The talk is based on joint work with McCoy and Baader, Lewark, and Liechti.