On diagrams of simplified trisections and mapping class groups

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)17-37
Number of pages21
JournalOsaka Journal of Mathematics
Volume57
Issue number1
Publication statusPublished - 2020 Jan

ASJC Scopus subject areas

  • Mathematics(all)

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