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

2016/10/21 by Tianjun Li, Li, Tian-Jun, Cheuk Yu Mak +1
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1610.06870

openalex publication_date 2016/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 2χ+3σ 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.

Citations

• Symplectic manifolds with contact type boundaries
• Holomorphic disks and topological invariants for closed three-manifolds
• On the complement of a positive normal crossing divisor with no triple intersection in a projective variety

Related

• Non-Exact Symplectic Cobordisms Between Contact 3-Manifolds
• On Symplectic Cobordisms
• A note on Stein fillings of contact manifolds
• Planar contact 3-manifolds with infinitely many Stein fillings
• The Kodaira dimension of diffeomorphic Kähler 3-folds