Abstract
We introduce the Kodaira dimension of contact 3-manifolds and establish some basic properties. Contact 3-manifolds with distinct Kodaira dimensions behave differently when it comes to the geography of various kinds of symplectic fillings. On the other hand, we also prove that, given any contact 3-manifold, there is a lower bound of 2x+3σ for all of its minimal symplectic fillings. This is motivated by Stipsicz's result in [38] for Stein fillings. Finally, we discuss various aspects of exact self-cobordisms of fillable contact 3-manifolds.
Original language | English (US) |
---|---|
Pages (from-to) | 5428-5449 |
Number of pages | 22 |
Journal | International Mathematics Research Notices |
Volume | 2020 |
Issue number | 17 |
DOIs | |
State | Published - Sep 1 2020 |
Bibliographical note
Publisher Copyright:© The Author(s) 2018.