The Kodaira Dimension of Contact 3-Manifolds and Geography of Symplectic Fillings

DOI10.1093/IMRN/RNY166zbMATH Open1460.53075arXiv1610.06870OpenAlexW2963372264MaRDI QIDQ5151563

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Publication date: 19 February 2021

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Abstract: We introduce the Kodaira dimension of contact 3-manifolds and establish some basic properties. In particular, contact 3-manifolds with distinct Kodaria dimensions behave differently when it comes to the geography of various kinds of fillings. On the other hand, we also prove that, given any contact 3-manifold, there is a lower bound of $2chi+3sigma$ for all its minimal symplectic fillings. This is motivated by the bound of Stipsicz for Stein fillings. Finally, we discuss various aspects of exact self cobordisms of fillable 3-manifolds.

Full work available at URL: https://arxiv.org/abs/1610.06870

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