Communications in Analysis and Geometry

Volume 31 (2023)

Number 10

Circular spherical divisor and their contact topology

Pages: 2235 – 2386

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n10.a2

Authors

Tian-Jun Li (School of Mathematics, University of Minnesota, Minneapolis, Minn., U.S.A.)

Cheuk Yu Mak (School of Mathematical Sciences, University of Southampton, United Kingdom)

Jie Min (Department of Mathematics and Statistics, University of Massachusetts, Amherst, Mass., U.S.A.)

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.

Received 16 February 2021

Accepted 9 November 2021

Published 13 August 2024