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## Discussion Tag Cloud

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• CommentRowNumber1.
• CommentAuthorjim_stasheff
• CommentTimeSep 15th 2013
Where is there anything written on the obstructions to a smooth manifold admitting a Poisson structure?
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeSep 15th 2013

Do you mean a Poisson bracket on the space of functions? Then there is no obstruction, as you can always take the Poisson bracket to constantly vanish.

• CommentRowNumber3.
• CommentAuthorjim_stasheff
• CommentTimeSep 15th 2013
I goofed. So what condition should I demand to avoid the trivial bracket?
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeSep 15th 2013
• (edited Sep 15th 2013)

Not sure what you need. The vanishing Poisson tensor has maximal kernel regarded as a map $\pi \colon \Gamma(T^\ast X) \longrightarrow \Gamma(T X)$. You could ask for a smaller kernel. If you ask for vanishing kernel, then you may want a symplectic manifold structure.