Chi-slice 3-braid links

Geometry Topology Seminar
Monday, August 30, 2021 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Jonathan Simone – Georgia Tech
John Etnyre

A link L in the 3-sphere is called chi-slice if it bounds a properly embedded surface F in the 4-ball with Euler characteristic 1. If L is a knot, then this definition coincides with the usual definition of sliceness. One feature of such a link L is that if the determinant of L is nonzero, then the double cover of the 3-sphere branched over L bounds a rational homology ball. In this talk, we will explore the chi-sliceness of 3-braid links. In particular, we will construct explicit families of chi-slice quasi-alternating 3-braids using band moves and we will obstruct the chi-sliceness of almost all other quasi-alternating 3-braid links by showing that their double branched covers do not bound rational homology 4-balls. This is a work in progress joint with Vitaly Brejevs.