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Sutured ECH is a natural invariant

We show that sutured embedded contact homology is a natural invariant of sutured contact 

 
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-manifolds which can potentially detect some of the topology of the space of contact structures on a 

 
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-manifold with boundary. The appendix, by C. H. Taubes, proves a compactness result for the completion of a sutured contact 

 
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-manifold in the context of Seiberg–Witten Floer homology, which enables us to complete the proof of naturality.