Contents Online
Mathematical Research Letters
Volume 29 (2022)
Number 6
Diagrams of $\star$-trisections
Pages: 1595 – 1658
DOI: https://dx.doi.org/10.4310/MRL.2022.v29.n6.a1
Authors
Abstract
In this note we provide a generalization for the definition of a trisection of a $4$-manifold with boundary. We demonstrate the utility of this more general definition by finding a trisection diagram for the Cacime Surface, and also by finding a trisection-theoretic way to perform logarithmic surgery. In addition, we describe how to perform $1$-surgery on closed trisections. The insight gained from this description leads us to the classification of an infinite family of genus three trisections. We include an appendix where we extend two classic results for relative trisections for the case when the trisection surface is closed.
Received 11 December 2019
Accepted 23 November 2020
Published 4 May 2023