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The Giroux Correspondence in dimension 3
- Publication Year :
- 2024
-
Abstract
- 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.<br />Comment: 19 pages, 10 figures
- Subjects :
- Mathematics - Geometric Topology
57K33
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2408.01079
- Document Type :
- Working Paper