Ribbon surfaces for alternating 3-braid closures

Vitalijs Brejevs (University of Glasgow)

Monday 22nd March 16:00-17:00 Online

Abstract


 One useful way of identifying non-slice knots amounts to showing that their double branched covers do not bound rational balls. The same method also obstructs links from being χ-slice, i.e., from bounding a properly embedded surface of Euler characteristic one with no closed components in the 4-ball. In this talk I will discuss recent work that builds on Jonathan Simone's classification of alternating 3-braid closures whose double branched covers bound rational balls, in which I exhibit several infinite families of χ-slice links among said closures and move one step closer to solving the slice-ribbon conjecture in this case. Time permitting, I will also discuss some ongoing joint work with Simone on quasi-alternating 3-braid closures.

The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/91412568415 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).


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