Characterizing Dehn surgeries on links via trisections

Abstract

We summarize and expand known connections between the study of Dehn surgery on links and the study of trisections of closed, smooth 4-manifolds. In particular, we propose a program in which trisections could be used to disprove the generalized property R conjecture, including a process that converts the potential counterexamples of Gompf, Scharlemann, and Thompson into genus four trisections of the standard 4-sphere that are unlikely to be standard. We also give an analog of the Casson–Gordon rectangle condition for trisections that obstructs reducibility of a given trisection.