Circular spherical divisors and their contact topology

TL;DR

This paper classifies certain circular spherical divisors in symplectic 4-manifolds, analyzes their contact topology, and determines properties of their minimal symplectic fillings, including Stein fillability and homology types.

Contribution

It provides a classification of concave circular spherical divisors up to toric equivalence and characterizes their symplectic and contact topologies, including Stein fillability and Betti number bounds.

Findings

All concave circular spherical divisors embed symplectically into closed symplectic 4-manifolds.

Such divisors are realized as symplectic log Calabi-Yau pairs if their complements are minimal.

Explicit Betti number bounds are given for Stein fillings when divisors are anticanonical and convex.

Abstract

This paper investigates the symplectic and contact topology associated to circular spherical divisors. We classify, up to toric equivalence, all concave circular spherical divisors $ D $ that can be embedded symplectically into a closed symplectic 4-manifold and show they are all realized as symplectic log Calabi-Yau pairs if their complements are minimal. We then determine the Stein fillability and rational homology type of all minimal symplectic fillings for the boundary torus bundles of such $D$. When $ D $ is anticanonical and convex, we give explicit betti number bounds for Stein fillings of its boundary contact torus bundle.