Sutured ECH is a natural invariant

Abstract

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.

131 pages, 9 figures; main article by Cagatay Kutluhan and Steven Sivek with an appendix by C. H. Taubes. v2: many changes, notably a new section 7 and appendix which complete the naturality proof; v3: many more changes following referee reports

References in corpus (1)

• Vanishing of the contact homology of overtwisted contact 3--manifolds

Cited by in corpus (3)

• Instanton Floer homology, sutures, and Heegaard diagrams
• Correction to a lemma in Embedded Contact Homology and Seiberg-Witten Floer Homology IV
• An exposition of the equivalence of Heegaard Floer homology and embedded contact homology