  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.
