On diagrams of simplified trisections and mapping class groups

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)17-37
ページ数21
ジャーナルOsaka Journal of Mathematics
57
1
出版ステータスPublished - 2020 1

ASJC Scopus subject areas

  • 数学 (全般)

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