The Giroux Correspondence in dimension 3

In an earlier paper, the authors proved the Giroux Correspondence for tight contact \(3\)-manifolds via convex Heegaard surfaces. Simultaneously, Breen, Honda and Huang gave an all-dimensions proof of the Giroux Correspondence by generalising convex surface theory to higher dimensions. This paper us...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Licata, Joan, Vértesi, Vera
Format: Article
Language:English
Subjects:
Manifolds (mathematics)
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In an earlier paper, the authors proved the Giroux Correspondence for tight contact \(3\)-manifolds via convex Heegaard surfaces. Simultaneously, Breen, Honda and Huang gave an all-dimensions proof of the Giroux Correspondence by generalising convex surface theory to higher dimensions. This paper uses a key result about relations of bypasses to complete the \(3\)-dimensional proof for arbitrary (not necessarily tight) contact 3-manifolds. This presentation features low-dimensional techniques and further clarifies the relationship between contact manifolds and their Heegaard splittings.
ISSN:2331-8422