On contact type hypersurfaces in 4-space
| Autor: | Mark, Thomas E., Tosun, Bülent |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00222-021-01083-9 |
| Popis: | We consider constraints on the topology of closed 3-manifolds that can arise as hypersurfaces of contact type in standard symplectic $R^4$. Using an obstruction derived from Heegaard Floer homology we prove that no Brieskorn homology sphere admits a contact type embedding in $R^4$, a result that has bearing on conjectures of Gompf and Koll\'ar. This implies in particular that no rationally convex domain in $C^2$ has boundary diffeomorphic to a Brieskorn sphere. We also give infinitely many examples of contact 3-manifolds that bound Stein domains but not symplectically convex ones; in particular we find Stein domains in $C^2$ that cannot be made Weinstein with respect to the ambient symplectic structure while preserving the contact structure on their boundaries. Comment: Adjusted exposition based on referee comments. Added results on planar contact structures and strong cobordisms to $S^3$ in section 5. Final version; published in Invent. Math |
| Databáze: | arXiv |
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