Characterizing Dehn surgeries on links via trisections

Jeffrey Meier; Alexander Zupan

doi:10.1073/pnas.1717187115

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arXiv · 1707.08955

Characterizing Dehn surgeries on links via trisections

Jeffrey Meier·Alexander Zupan

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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.

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Jeffrey Meier, Alexander Zupan. 2017-07-27. Characterizing Dehn surgeries on links via trisections. https://doi.org/10.1073/pnas.1717187115

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