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Sur une généralisation de la notion de V-variété

Elisa Prato
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Abstract

Nous considérons un espace topologique qui est localement isomorphe au quotient de R^k par l'action d'un groupe discret et nous l'appelons quasi-variété de dimension k. Les quasi-variétés généralisent les variétés et les V-variétés et représentent le cadre naturel pour la réduction symplectique par rapport à l'action induite d'un sous-groupe de Lie, compact ou non, d'un tore. Nous définissons les quasi-tores, les actions hamiltoniennes de quasi-tores et l'application moment sur une quasi-variété symplectique, et nous montrons que tout polytope convexe simple, rationnel ou non, est l'image de l'application moment pour l'action d'un quasi-tore sur une quasi-variété.

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Elisa Prato. 1999-04-30. Sur une généralisation de la notion de V-variété. https://doi.org/10.1016/s0764-4442(99)80291-2

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