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arXiv · 1008.2734

Embedded contact homology and open book decompositions

Vincent Colin·Paolo Ghiggini·Ko Honda
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Abstract

This is the first of a series of papers devoted to proving the equivalence of Heegaard Floer homology and embedded contact homology (abbreviated ECH). In this paper we prove that, given a closed, oriented, contact $3$-manifold, there is an equivalence between ECH of the closed $3$-manifold and a version of ECH, defined on the complement of the binding of an adapted open book decomposition. In the appendix we give a full proof of the Morse-Bott gluing result that we need in this article and in the subsequent ones of the series proving the isomorphism between Heegaard Floer homology and ECH. V.8: we fixed a mistake in the appendix and added Yuan Yao as a coauthor.

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Vincent Colin, Paolo Ghiggini, Ko Honda. 2010-08-16. Embedded contact homology and open book decompositions. https://doi.org/10.2140/gt.2025.29.3345

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