Loading…

Reeb flows without simple global surfaces of section

We construct, for any given positive integer \(n\), Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than \(n\) boundary components. We use a connected sum operation for open books to construct such systems. We prove that this property is sta...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-07
Main Authors: Kim, Juno, Kim, Yonghwan, Otto van Koert
Format: Article
Language:English
Subjects:
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We construct, for any given positive integer \(n\), Reeb flows on contact integral homology 3-spheres which do not admit global surfaces of section with fewer than \(n\) boundary components. We use a connected sum operation for open books to construct such systems. We prove that this property is stable with respect to \(C^{4+\epsilon}\)-small perturbations of the Hamiltonian given on the symplectization.
ISSN:2331-8422
DOI:10.48550/arxiv.2104.03728