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Embedded contact homology
and open book decompositions
Vincent Colin, Paolo Ghiggini and Ko HondaAppendix: Vincent Colin, Paolo Ghiggini, Ko Honda and Yuan Yao |
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Geometry & Topology 29 (2025) 3345–3463
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Abstract |
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Given a closed oriented contact -manifold , we prove an equivalence between the embedded contact homology of and a version of embedded contact homology “relative to the boundary”, defined on the complement of a tubular neighborhood of a null-homologous knot. This paper can be viewed as the first of a series of papers devoted to proving the isomorphism between Heegaard Floer homology and embedded contact homology. The appendix, written jointly with Yuan Yao, gives a complete proof of Morse–Bott gluing for one-level cascades in embedded contact homology. |
Keywords
contact structure, Reeb dynamics, embedded contact
homology, open book decompositions
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Mathematical Subject Classification
Primary: 57K31, 57K33
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References |
Publication
Received: 13 April 2020
Revised: 20 August 2023
Accepted: 28 October 2023
Published: 10 October 2025
Proposed: András I Stipsicz
Seconded: Peter Ozsváth, Ciprian Manolescu
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Authors |
| Vincent Colin | |
| Laboratoire de Mathématiques Jean
Leray Nantes Université Nantes France |
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| Paolo Ghiggini | |
| Laboratoire de Mathématiques Jean
Leray Nantes Université Nantes France |
Institut Fourier Université Grenoble Alpes Grenoble France |
| Ko Honda | |
| Department of Mathematics University of California, Los Angeles Los Angeles, CA United States |
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| http://www.math.ucla.edu/~honda | |
| Yuan Yao | |
| Department of Mathematics University of California, Berkeley Berkeley, CA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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