Cotangent Microbundle Category, I

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dc.creatorCattaneo, Alberto S.
dc.creatorDherin, Benoit
dc.creatorWeinstein, Alan
dc.date2007-12-10
dc.date.accessioned2026-07-07T08:48:13Z
dc.date.available2026-07-07T08:48:13Z
dc.descriptionWe define a local version of the extended symplectic category, the cotangent microbundle category, MiC, which turns out to be a true monoidal category. We show that a monoid in this category induces a Poisson manifold together with the local symplectic groupoid integrating it. Moreover, we prove that monoid morphisms produce Poisson maps between the induced Poisson manifolds in a functorial way. This gives a functor between the category of monoids in MiC and the category of Poisson manifolds and Poisson maps. Conversely, the semi-classical part of the Kontsevich star-product associated to a real-analytic Poisson structure on an open subset of R^n produces a monoid in MiC.
dc.description32 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/0712.1385
dc.identifierhttp://arxiv.org/abs/0712.1385
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/143868
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subject81S10; 53D55; 53D50
dc.titleCotangent Microbundle Category, I
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