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Seminar

FHT Program Seminar: Symmetry and Sliceness September 29, 2022 (09:00 AM PDT - 09:45 AM PDT)
Parent Program:
Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Abhishek Mallick (Max-Planck-Institut für Mathematik)
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FHT Program Seminar: Symmetry And Sliceness

Abstract/Media

To participate in this seminar, please register HERE.

A knot is called slice if it bounds a smoothly embedded disk in the four-ball. Much of low-dimensional topology revolves around obstructing this property of a knot. In this talk, we will introduce a method of obstructing sliceness which takes into account the actions of different symmetries on the Floer homology group. Using this, we will show that the (2,1)-cable of the figure-eight knot is not slice, answering a 42-year-old question posed by Kawauchi. Historically, this knot gained particular interest since it was regarded as one of the simplest "potential" counter-example to the slice-ribbon conjecture. Our proof also shows that the branched double cover of the aforementioned knot is a cork. This is joint work with Dai, Kang, Park, and Stoffregen.

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FHT Program Seminar: Symmetry And Sliceness