Affiliation:
U of Cambridge/MPI
Date:
Mon, 11/10/2010 - 18:00 - 19:00
We introduce quilted Floer homology (QFH), a new invariant of 3-manifolds equipped with an indefinite circle valued Morse function (i.e. broken fibration). This is yet another localization of Seiberg-Witten theory and a natural extension of Perutz's 4-manifold invariants associated with broken Lefschetz fibrations, making it a (3+1) theory. We relate Perutz's theory to Heegaard Floer theory by giving an isomorphism between QFH and HF+ for extremal spin^c structures with respect to the fibre of the Morse function.