2007/12/10 by Alberto S. Cattaneo, Benoit Dherin, Cattaneo, Alberto S. +3
Mathematics · Physics and Astronomy · #53D50 #53D55 #81S10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #msc:53D50 #msc:53D55 #msc:81S10
paper · pdf · doi:10.48550/arxiv.0712.1385
32 pages, 5 figures
arxiv created 2007/12/10 · arxiv updated 2009/12/01
We 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 Rn produces a monoid in MiC.