Quasifold groupoids and diffeological quasifolds

Abstract: A quasifold is a space that is locally modeled by quotients of R^n by countable group actions. These arise in Elisa Prato's generalization of the Delzant theorem to irrational polytopes, and include orbifolds and manifolds. We approach quasifolds in two ways: by viewing them as diffeological spaces, we form the category of diffeological quasifolds, and by viewing them as Lie groupoids (with bibundles as morphisms), we form the category of quasifold groupoids. We show that, restricting to effective groupoids, and locally invertible morphisms, these two categories are equivalent. In particular, an effective quasifold groupoid is determined by its diffeological orbit space. This is join work with Yael Karshon.

differential geometrydynamical systemsgeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and Dynamics seminar

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