Symplectic Divisorial Capping in Dimension 4

Abstract

We investigate the notion of symplectic divisorial compactification for symplectic 4-manifolds with either convex or concave type boundary. This is motivated by the notion of compactifying divisors for open algebraic surfaces. We give a sufficient and necessary criterion, which is simple and also works in higher dimensions, to determine whether an arbitrarily small concave/convex neighborhood exist for an $\omega$-orthogonal symplectic divisor (a symplectic plumbing). If deformation of symplectic form is allowed, we show that a symplectic divisor has either a concave or convex neighborhood whenever the symplectic form is exact on the boundary of its plumbing. As an application, we classify symplectic compactifying divisors having finite boundary fundamental group. We also obtain a finiteness result of fillings when the boundary can be capped by a symplectic divisor with finite boundary fundamental group.

66 pages. More complete results obtained. Comments welcomed

References in corpus (8)

• Lefschetz pencils and divisors in moduli space
• Lectures on Exotic Algebraic Structures on Affine Spaces
• A biased view of symplectic cohomology
• Canonical contact structures on some singularity links
• Normal complex surface singularities with rational homology disk smoothings
• On the symplectic invariance of log Kodaira dimension
• Symplectic fillings of Seifert fibered spaces
• Reeb orbits and the minimal discrepancy of an isolated singularity

Cited by in corpus (7)

• Calabi-Yau Caps, Uniruled Caps and Symplectic Fillings
• On Stein fillings of contact torus bundles
• The Kodaira dimension of contact 3-manifolds and geography of symplectic fillings
• Geometry of symplectic log Calabi-Yau pairs
• Symplectic log Calabi-Yau surface---deformation class
• Strong symplectic fillability of contact torus bundles
• Intersection of almost complex submanifolds