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Pré-Publication, Document De Travail Année : 2015

Cotangent paths as coisotropic subsets for local functions

Yahya Turki
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Résumé

We establish a local function version of a classical result claiming that a bivector field on a manifold M is Poisson if and only if cotan-gent paths form a coisotropic set of the infinite dimensional symplectic manifold of paths valued in T * M. Our purpose here is to prove this result without using the Banach manifold setting, setting which fails in the periodic case because cotangent loops do not form a Banach sub-manifold. Instead, we use local functions on the path space, a point of view that allows to speak of a coisotropic set.
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Dates et versions

hal-01285645 , version 1 (09-03-2016)

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  • HAL Id : hal-01285645 , version 1

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Camille Laurent-Gengoux, Yahya Turki. Cotangent paths as coisotropic subsets for local functions. 2015. ⟨hal-01285645⟩
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