Embedded contact homology and open book decompositions
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arXiv
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| Format: | Preprint |
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2010
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| _version_ | 1866914091565580288 |
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| author | Colin, Vincent Ghiggini, Paolo Honda, Ko |
| author_facet | Colin, Vincent Ghiggini, Paolo Honda, Ko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1008_2734 |
| institution | arXiv |
| publishDate | 2010 |
| record_format | arxiv |
| spellingShingle | Embedded contact homology and open book decompositions Colin, Vincent Ghiggini, Paolo Honda, Ko Symplectic Geometry 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. |
| title | Embedded contact homology and open book decompositions |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/1008.2734 |