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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.

43 votes
7 answers
6k views

Why should I care about Heegaard-Floer theory?

I would like to collect a list of applications of Heegaard-Floer theory. By applications, I don't mean things like "it can detect the unknot" or "it can detect knot genus". Algorithms for these kind …