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Induced differential forms on manifolds of functions

Cornelia Vizman (2011)

Archivum Mathematicum

Differential forms on the Fréchet manifold ( S , M ) of smooth functions on a compact k -dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hat pairing. Special cases are the transgression map Ω p ( M ) Ω p - k ( ( S , M ) ) (hat pairing with a constant function) and the bar map Ω p ( M ) Ω p ( ( S , M ) ) (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].

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