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Title:
Naturality of Heegaard Floer homology
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Abstract:
Previously, the Heegaard Floer invariants of 3-manifolds and links have only been defined up to isomorphism. This suffices for many applications, but to be able to talk about diffeomorphism or cobordism maps on such groups one needs a functorial construction. We will provide the missing ingredient for functoriality, and define the action of the based mapping class group. Our approach relies on the bifurcation analysis of 2-parameter families of gradient vector fields. As it turns out, the hat version of HF depends on the choice of basepoint, but the other flavors do not. This is joint work with Dylan Thurston and Peter Ozsváth.
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