Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Round fold maps on $3$–manifolds

Naoki Kitazawa and Osamu Saeki

Algebraic & Geometric Topology 23 (2023) 3745–3762
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

Open Access made possible by participating institutions via Subscribe to Open.