We show that sutured embedded contact homology is a natural invariant of sutured contact 3-manifolds which can potentially detect some of the topology of the space of contact structures on a 3-manifold with boundary. The appendix, by C. H. Taubes, proves a compactness result for the completion of a sutured contact 3-manifold in the context of Seiberg-Witten Floer homology, which enables us to complete the proof of naturality.
Author(s): agatay Kutluhan, Steven Sivek, C. H. Taubes
Series: Memoirs of the American Mathematical Society, 1350
Publisher: American Mathematical Society
Year: 2022
Language: English
Pages: 147
City: Providence
Cover
Title page
Chapter 1. Introduction
1.1. Organization
1.2. Acknowledgments
Chapter 2. Sutured ECH and some related constructions
2.1. Sutured ECH
2.2. Contact 1-handles
2.3. Liouville forms on the boundary
2.4. Closed manifolds and continuation maps
Chapter 3. Independence of the almost complex structure
Chapter 4. Independence of the contact form
4.1. An isomorphism for isotopic contact forms
4.2. Isomorphisms and embedding data
4.3. A natural version of Theorem 4.5
Chapter 5. Some properties of the contact class
Chapter 6. Invariance under gluing 1-handles
Chapter 7. Stabilization and a canonical version of sutured ECH
Appendix A. Appendix by C. H. Taubes
A.1. Setting the stage
A.2. Monopoles
A.3. Instantons
A.4. A priori bounds for instantons
A.5. Local convergence to pseudo-holomorphic curves
A.6. Convergence of instantons as ?→∞
A.7. Comparing instantons on ?_{∞} and ?_{?}
Bibliography
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