Sphere-bundles
- most commonly, circle-bundles - enter symplectic geometry as
coisotropic submanifolds fibred by spheres: these define Lagrangians in
product manifolds. The classical Gysin sequence describes the
homology of a sphere-bundle. I will describe Floer-theoretic
Gysin sequences (related results have been obtained independently by Biran-Khanevsky). These sequences are set up using the theory of "pseudo-holomorphic quilts". Motivating examples fit into my project to set up symplectic models for Seiberg-Witten or instanton gauge theory on 3-manifolds with circle-valued Morse functions.
