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January 2020 On diagrams of simplified trisections and mapping class groups
Kenta Hayano
Osaka J. Math. 57(1): 17-37 (January 2020).


A simplified trisection is a trisection map on a 4--manifold such that, in its critical value set, there is no double point and cusps only appear in triples on innermost fold circles. We give a necessary and sufficient condition for a 3--tuple of systems of simple closed curves in a surface to be a diagram of a simplified trisection in terms of mapping class groups. As an application of this criterion, we show that trisections of spun 4--manifolds due to Meier are diffeomorphic (as trisections) to simplified ones. Baykur and Saeki recently gave an algorithmic construction of a simplified trisection from a directed broken Lefschetz fibration. We also give an algorithm to obtain a diagram of a simplified trisection derived from their construction.


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Kenta Hayano. "On diagrams of simplified trisections and mapping class groups." Osaka J. Math. 57 (1) 17 - 37, January 2020.


Published: January 2020
First available in Project Euclid: 15 January 2020

zbMATH: 07196613
MathSciNet: MR4052626

Primary: 57R45
Secondary: 20F38, 57M99, 57R65

Rights: Copyright © 2020 Osaka University and Osaka City University, Departments of Mathematics


Vol.57 • No. 1 • January 2020
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