No Brieskorn homology sphere admits a contact type embedding in R^4, with consequences for rationally convex domains in C^2 and distinctions between Stein and Weinstein structures.
The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I
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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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On contact type hypersurfaces in 4-space
No Brieskorn homology sphere admits a contact type embedding in R^4, with consequences for rationally convex domains in C^2 and distinctions between Stein and Weinstein structures.