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

TL;DR

This paper characterizes when certain chain link surgeries bound rational homology balls, introduces a practical lattice-theoretic obstruction method, and extends slice--ribbon conjecture results to quasi-alternating 3-braid links.

Contribution

It develops a practical approach to compute the lattice-theoretic cubiquity obstruction and applies it to prove a generalized slice--ribbon conjecture for quasi-alternating 3-braid links.

Findings

Identifies surgeries on chain links bounding rational homology balls.

Provides a method to compute the cubiquity obstruction.

Proves the slice--ribbon conjecture for all but one family of quasi-alternating 3-braid links.

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.