Geodesic
Induced differential forms on manifolds of functions
Archivum mathematicum, Tome 47 (2011) no. 3, pp. 201-215.

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Differential forms on the Fréchet manifold $\mathcal{F}(S,M)$ 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 $\Omega ^p(M)\rightarrow \Omega ^{p-k}(\mathcal{F}(S,M))$ (hat pairing with a constant function) and the bar map $\Omega ^p(M)\rightarrow \Omega ^p(\mathcal{F}(S,M))$ (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].
Classification : 11K11, 22C22
Keywords: manifold of functions; fiber integral; diffeomorphism group 
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     author = {Vizman, Cornelia},
     title = {Induced differential forms on manifolds of functions},
     journal = {Archivum mathematicum},
     pages = {201--215},
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     url = {http://geodesic.mathdoc.fr/item/ARM_2011__47_3_a2/}
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Vizman, Cornelia. Induced differential forms on manifolds of functions. Archivum mathematicum, Tome 47 (2011) no. 3, pp. 201-215. http://geodesic.mathdoc.fr/item/ARM_2011__47_3_a2/