Explicit concave fillings of contact three-manifolds

Abstract

In this paper we give explicit, handle-by-handle constructions of concave symplectic fillings of all closed, oriented contact 3-manifolds. These constructions combine recent results of Giroux relating contact structures and open book decompositions of 3-manifolds, earlier results of the author on attaching 4-dimensional symplectic 2-handles along transverse links, and some tricks with mapping class groups of compact surfaces with non-empty boundary.

15 pages. Accepted for publication in the Mathematical Proceedings of the Cambridge Philosophical Society. Current version is identical to final version submitted to the journal, differs from original version only in some notation and minor editorial changes

References in corpus (1)

• On the topology of compact Stein surfaces

Cited by in corpus (7)

• Holomorphic disks and genus bounds
• Four-dimensional symplectic cobordisms containing three-handles
• Constructing symplectic forms on 4-manifolds which vanish on circles
• On symplectic fillings
• Kahler decomposition of 4-manifolds
• Open books and configurations of symplectic surfaces and erratum
• Planarity in higher-dimensional contact manifolds