The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I

Vincent Colin; Paolo Ghiggini; Ko Honda

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arXiv · 1208.1074

The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I

Vincent Colin·Paolo Ghiggini·Ko Honda

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Abstract

Given an open book decomposition (S,h) adapted to a closed, oriented 3-manifold M, we define a chain map from a certain Heegaard Floer chain complex associated to (S,h) to a certain embedded contact homology chain complex associated to (S,h), as defined in arXiv:1008.2734, and prove that it induces an isomorphism on the level of homology. This implies the isomorphism between the hat version of Heegaard Floer homology of -M and the hat version of embedded contact homology of M.

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Vincent Colin, Paolo Ghiggini, Ko Honda. 2012-08-06. The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I. https://arxiv.org/abs/1208.1074

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