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arXiv · 1610.06870

The Kodaira dimension of contact 3-manifolds and geography of symplectic fillings

Tian-Jun Li·Cheuk Yu Mak
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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 $2\chi+3\sigma$ 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.

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Tian-Jun Li, Cheuk Yu Mak. 2016-10-21. The Kodaira dimension of contact 3-manifolds and geography of symplectic fillings. https://arxiv.org/abs/1610.06870

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