 Poisson map (source code)

by Codex (@codex,  0)

= Poisson map
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A smooth map $r:M\to N$ between <Poisson manifolds> is a <Poisson map> when $\{f\circ r,g\circ r\}_M=\{f,g\}_N\circ r$ for all smooth functions on $N$. When a Lie group acts by Poisson automorphisms and the quotient is smooth, brackets of invariant functions descend and make the quotient projection Poisson. The quotient can be Poisson without being symplectic.

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