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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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What is the Heegaard Floer Homology of a connect sum of $S^2 \times S^1$s?
The explicit calculation of this Heegaard-Floer homology (at least, $HF^-$, and of the unique $\text{Spin}^c$ structure for which $c_1(\mathfrak s) = 0$) was carried out in the paper in which it was i …