2022/01/19 by Noémie C. Combe, Noemie Combe, Combe, Noemie +5
Computer Science · Engineering · Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #Engineering #FOS: Mathematics #Frobenius theorem (differential topology) #Geometry #Geometry and topology #Homotopy and Cohomology in Algebraic Topology #Information geometry #Linguistics #Manifold (fluid mechanics) #Mathematics #Philosophy #Poisson algebra #Poisson bracket #Poisson distribution #Poisson manifold #Pure mathematics #Statement (logic) #Statistical manifold #Symplectic Geometry (math.SG) #Symplectic geometry #Symplectic manifold #Symplectomorphism #Topological and Geometric Data Analysis #math.AG #math.DG #math.SG
paper · pdf · doi:10.48550/arxiv.2201.07517
arxiv created 2022/01/19 · openalex publication_date 2022/01/19 · arxiv updated 2022/01/20 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/04
We prove that the information geometry's Frobenius manifold is a symplectic manifold having Poisson structures. By proving this statement, a bridge is created between the theories developed by Vinberg, Souriau and Koszul and the Frobenius manifold approach. Until now these approaches seemed disconnected.