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Hamiltonian systems, symplectic flows, classical integrable systems

10 votes
Accepted

Wanted: differential coming from higher genus surface in Heegaard Floer homology

Yes, $S \to \Sigma$ can fail to be an immersion. The failure is a branch point of the map $S \to \Sigma$, since it is (close to) a holomorphic map. This is fairly common as soon as the multiplicity …
Dylan Thurston's user avatar
12 votes
Accepted

Maslov index and Heegard Floer homology

Robert Lipshitz has the nicest formula, described in Corollary 4.3 of this paper: Robert Lipshitz, A cylindrical reformulation of Heegaard Floer homology, Geometry & Topology 10 (2006) 955–1096, DOI: …
Dylan Thurston's user avatar
5 votes

Is there a version of Seiberg-Witten-Floer or Heegard-Floer homology for 3-manifolds with bo...

Andy Manion has already plugged our answer for Heegaard Floer homology. On the Seiberg-Witten side, not as much is known, but Tim Nguyen's thesis starts to attack the problem. However, there isn't a …
Dylan Thurston's user avatar