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A new infinite order formulation of variational sequences

Raffaele Vitolo (1998)

Archivum Mathematicum

The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition...

De Rham cohomology and homotopy Frobenius manifolds

Vladimir Dotsenko, Sergey Shadrin, Bruno Vallette (2015)

Journal of the European Mathematical Society

We endow the de Rham cohomology of any Poisson or Jacobi manifold with a natural homotopy Frobenius manifold structure. This result relies on a minimal model theorem for multicomplexes and a new kind of a Hodge degeneration condition.



Communications in Mathematics

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