Round fold maps on 3–manifolds

Kitazawa, Naoki; Saeki, Osamu

doi:10.2140/agt.2023.23.3745

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Round fold maps on $3$–manifolds

Naoki Kitazawa and Osamu Saeki

Algebraic & Geometric Topology 23 (2023) 3745–3762

DOI: 10.2140/agt.2023.23.3745

Abstract

We show that a closed orientable $3$ –dimensional manifold admits a round fold map into the plane, ie a fold map whose critical value set consists of disjoint simple closed curves isotopic to concentric circles, if and only if it is a graph manifold, generalizing the characterization for simple stable maps into the plane. Furthermore, we also give a characterization of closed orientable graph manifolds that admit directed round fold maps into the plane, ie round fold maps such that the number of regular fiber components of a regular value increases toward the central region in the plane.

Dedicated to Professor Kazuhiro Sakuma on the occasion of his 60th birthday

Keywords

round fold map, graph manifold, simple stable map, 3–manifold, cohomology ring, normal form plumbing graph

Mathematical Subject Classification

Primary: 57R45

Secondary: 57K30, 58K30

References

Publication

Received: 7 September 2021

Revised: 29 March 2022

Accepted: 14 July 2022

Published: 5 November 2023

Authors

Naoki Kitazawa
Institute of Mathematics for Industry Kyushu University Fukuoka Japan

Osamu Saeki
Institute of Mathematics for Industry Kyushu University Fukuoka Japan

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Volume 23, issue 8 (2023)