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 addition, we describe how the potential counterexamples to the Generalized Property R Conjecture given by Gompf, Scharlemann, and Thompson yield genus four trisections of the standard four-sphere that are unlikely to be standard. Finally, we give an analog of the Casson- Gordon Rectangle Condition for trisections that can be used to obstruct reducibility of a given trisection.

15 pages, 4 color figures. Comments welcome!

References in corpus (2)

• Classification of trisections and the Generalized Property R Conjecture
• Genus two trisections are standard

Cited by in corpus (3)

• Doubly pointed trisection diagrams and surgery on 2-knots
• Trisections and spun 4-manifolds
• Thin Position through the lens of trisections of 4-manifolds