set 1 is an extremely addictive, fast-paced card game found in toy stores nationwide. Although children often beat adults, the game has a rich mathematical structure linking it to the combinatorics of finite affine and projective spaces and the theory of error-correcting codes. Last year an unexpected connection to Fourier analysis was used to settle a… (More)
Several known constructions of phase spaces are merged into the framework of Poisson fiber bundles and coupling Dirac structures. Functorial properties of our construction are discussed and examples are provided. Finally, applications to fibered symplectic groupoids are given.
We give an intrinsic proof that Vorobjev's first approximation of a Poisson manifold near a symplectic leaf is a Poisson manifold. We also show that Conn's linearization results cannot be extended in Vorob-jev's setting.
We give lower bounds on the Poisson embedding dimension of a singular quotient of a symplectic manifold by doing a local calculation in formal power series. In particular, we show that the Poisson embedding dimension of the weight-(1,1,2) resonance space is at least 13. 1991 MSC: 17B63, 53D.