User eigenbunny - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T03:53:30Z http://mathoverflow.net/feeds/user/16333 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/69888/cohomology-theory-for-symplectic-manifolds/69903#69903 Answer by Eigenbunny for Cohomology theory for symplectic manifolds Eigenbunny 2011-07-09T19:36:22Z 2011-07-09T19:36:22Z <p>How about looking at the homology of the homotopy fibre of the map $M \rightarrow K(\mathbb R,2)$ which represents your cohomology class? At least, any Lagrangian submanifold $L$ has the property that $L \rightarrow M \rightarrow K(\mathbb R,2)$ is (canonically) nullhomotopic, so gives rise to a homology class in the homotopy fibre. Absolutely no warranty that this is helpful ...</p> <p>(... in fact, maybe you'd better look in the direction of Chern-Simons differential cocycles)</p>