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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.
17
votes
Why should I care about Heegaard-Floer theory?
Ghiggini has shown that the only knot giving rise to the Poincare homology sphere by Dehn filling is the trefoil knot, as an application of Heegaard Floer homology.
Another important point is that n …
7
votes
Three-manifolds having a Reebless foliation but not a taut one
I don't have definitive answers to your questions, but I'll try to make some comments.
For 1), I haven't done a literature search to see if this was known. However, Boyer and Clay propose a related op …