How to recognise a 4-ball when you see one

Abstract

We apply the method of filling with holomorphic discs to a 4-dimensional symplectic cobordism with the standard contact 3-sphere as a convex boundary component. We establish the following dichotomy: either the cobordism is diffeomorphic to a ball, or there is a periodic Reeb orbit of quantifiably short period in the concave boundary of the cobordism. This allows us to give a unified treatment of various results concerning Reeb dynamics on contact 3-manifolds, symplectic fillability, the topology of symplectic cobordisms, symplectic non-squeezing, and the non-existence of exact Lagrangian surfaces in standard symplectic 4-space.

26 pages, 2 figures; v2: minor changes and corrections; v3: proof of Lemma 6.2 corrected

References in corpus (1)

• Weak Symplectic Fillings and Holomorphic Curves

Cited by in corpus (11)

• The topology of Stein fillable manifolds in high dimensions I
• Gromov compactness for holomorphic discs with totally real boundary conditions
• The topology of Stein fillable manifolds in high dimensions II
• Reeb dynamics detects odd balls
• Polyfolds, Cobordisms, and the strong Weinstein conjecture
• Discontinuous symplectic capacities
• Periodic orbits in virtually contact structures
• Symplectic dynamics of contact isotropic torus complements
• Combinatorial Reeb dynamics on punctured contact 3-manifolds
• Analytic filling of totally real tori
• Lectures on controlled Reeb dynamics