Heegaard Floer homology of broken fibrations

Yanki Lekili (University of Cambridge)

Monday 17th October, 2011 15:00-16:00 416


Heegaard Floer homology (HF+) is a powerful 3-manifold invariant defined by Ozsvath and Szabo as a Lagrangian intersection theory. We will first review the original definition. Then, we will describe a new variant construction which uses an indefinite circle valued Morse function instead of an self-indexing Morse function as an auxilary data. This new variant will be called quilted Floer homology (QFH). QFH is an extension of Perutz's 4-manifold invariants making it a 3+1 theory. Our main result is an isomorphism between QFH and HF+ for extremal spin^c structures with respect to the fibre of the Morse function. Time permitting, I will discuss applications including: new computations of Heegaard Floer homology and a characterization of sutured Floer homology.

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