Poisson structure on manifolds with corners

2016/01/01 by Joel Antonio-Vásquez, Antonio-Vásquez, Joel
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1601.00089

arxiv created 2016/01/01 · openalex publication_date 2016/01/01 · arxiv updated 2016/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Since a Poisson Structure is a smooth bivector field, we use a ring-valued sheaf \OO_X on a manifold with corners X, we can interpret \OO_X(U) as the ring of admissible smooth functions where U is an open subset on X, in this way, a poisson structure on (X, \OO_X) is a sheaf morphism \-, -\: \OO_X × \OO_X \longrightarrow \OO_X which satisfies the Leibniz rule an also the Jacobi Identity.

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