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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.
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Path of almost complex structure in the definition of Heegaard Floer homology
$\DeclareMathOperator\Sym{Sym}$In order to define Heegaard Floer Homology for a connected, closed, oriented 3 manifold, we fix a generic path of nearly symmetric almost complex structure $J_s$ over $\ …