On chain link surgeries bounding rational homology balls and $\chi$-slice 3-braid closures

Abstract

We determine which integral surgeries on a large class of circular chain links bound rational homology balls. Our key tool is the lattice-theoretic cubiquity obstruction recently developed by Greene and Owens. We discuss a practical method of computing it, and, as an application, prove that a generalisation of the slice--ribbon conjecture holds for all but one infinite family of quasi-alternating 3-braid links. This extends previous results of Lisca concerning the conjecture for 3-braid knots.

Final version; to appear in Transactions of the AMS. 22 figures, 9 of which are full-page figures