  We use the theory of pseudo-holomorphic quilts to establish a counterpart, in
symplectic Floer homology, to the Gysin sequence for the homology of a
sphere-bundle. In a motivating class of examples, this "symplectic Gysin
sequence" is precisely analogous to an exact sequence describing the behaviour
of Seiberg-Witten monopole Floer homology for 3-manifolds under connected sum.
