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Sutured ECH is a natural invariant

About this Title

Çağatay Kutluhan, Steven Sivek and C. H. Taubes

Publication: Memoirs of the American Mathematical Society
Publication Year: 2022; Volume 275, Number 1350
ISBNs: 978-1-4704-5054-0 (print); 978-1-4704-7016-6 (online)
Published electronically: December 22, 2021

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Table of Contents


  • 1. Introduction
  • 2. Sutured ECH and some related constructions
  • 3. Independence of the almost complex structure
  • 4. Independence of the contact form
  • 5. Some properties of the contact class
  • 6. Invariance under gluing 1-handles
  • 7. Stabilization and a canonical version of sutured ECH
  • A. Appendix by C. H. Taubes


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.

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