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For questions about Heegaard-Floer homology (as introduced by Ozsváth-Szabó in 2003) and its uses in 3- and 4-dimensional topology.
4
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Path of almost complex structure in the definition of Heegaard Floer homology
According to Proposition 3.9 of Ozsvath and Szabo's original paper "Holomorphic disks and topological invariants for closed three-manifolds" there are indeed topological conditions one can put on the …