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Graph cobordisms and Heegaard Floer homology IAN ZEMKEWe construct a graph TQFT for the minus flavor of Heegaard Floer homology.Our graph TQFT extends Ozsvth and Szab's TQFT for closed and connected 3-manifolds, and assigns maps to cobordisms with disconnected ends.As an application, we give an explicit formula for the chain homotopy type of the 1 -action on Heegaard Floer homology.We show that on homology the 1 -action is trivial on the plus, minus and infinity flavors, but give examples where it is nontrivial on the hat flavor.HF .Y; s/; HF 1 .Y; s/; HF C .Y; s/ and c HF.Y; s/; which are modules over the ring F 2 OEU .These modules fit into the framework of a .3C1/-dimensional
Ian Zemke (Mon,) studied this question.