Osaka Journal of Mathematics

On diagrams of simplified trisections and mapping class groups

Kenta Hayano

Abstract

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.

Article information

Source
Osaka J. Math., Volume 57, Number 1 (2020), 17-37.

Dates
First available in Project Euclid: 15 January 2020

https://projecteuclid.org/euclid.ojm/1579079109

Mathematical Reviews number (MathSciNet)
MR4052626

Citation

Hayano, Kenta. On diagrams of simplified trisections and mapping class groups. Osaka J. Math. 57 (2020), no. 1, 17--37. https://projecteuclid.org/euclid.ojm/1579079109

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