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Feb 10, 2010 at 10:19 comment added jvkersch 1) You're absolutely right: the other "generator" that I mentioned in my question is of course homologous to the boundary, hence zero. This also puts an end to much of my confusion about relative homology, so thanks again! 2-3) You're right about volume vs. symplectic manifolds. I'm trying to formalize some construction in Arnold's book on Topological Fluid Dynamics, so luckily volume-preserving maps are what I need. Putting it in the context of manifolds with a volume form gives me a pointer of where to look for references -- I remember seeing a flux homomorphism for volume manifolds...
Feb 10, 2010 at 10:14 vote accept jvkersch
Feb 9, 2010 at 22:04 history answered Dmitri Panov CC BY-SA 2.5