Heegaard Floer homology of broken fibrations over the circle

Details Heegaard Floer homology of broken fibrations over the circle Heegaard Floer homology of broken fibrations over the circle

2009-03-10

arxiv.org/abs/0903.1773v3

Mathematics

Symplectic Geometry

33 pages, 3 figures. An unnecessary technical assumption is removed

Scientific paper

We discover a strong relation between Perutz's Lagrangian matching invariants and Ozsvath-Szabo's Heegaard Floer invariants of three and four manifolds. In this paper, we make this relation explicit by proving an isomorphism of 3--manifold invariants for extremal spin^c structures. As applications, we give new calculations of Heegaard Floer homology of certain classes of 3--manifolds, a characterization of Juhasz's sutured Floer homology and a proof of Floer's excision theorem in the context of Heegaard Floer homology.

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