A four-dimensional mapping class group relation

Abstract

In the symplectic mapping class group of a $4$-dimensional Weinstein domain, we give a relation between two products of (right-handed) Dehn twists via holomorphic curve techniques. A key ingredient of the construction is a solution to the symplectic isotopy problem on symplectic submanifolds in del Pezzo surfaces. In the appendix, we provide an alternative proof of a relation between a fibered Dehn twist and a product of Dehn twists.

33 pages, 3 figures. Accepted for publication in Mathematische Annalen

References in corpus (8)

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• Dehn twists and free subgroups of symplectic mapping class groups
• Lectures on Holomorphic Curves in Symplectic and Contact Geometry
• Pseudoholomorphic curves and the symplectic isotopy problem
• Lecture notes on stabilization of contact open books
• The gluing construction for normally generic J-holomorphic curves
• Maximal contact and symplectic structures
• Symplectic Mapping Class Group Relations Generalizing the Chain Relation