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Keywords:
manifold of functions; fiber integral; diffeomorphism group
manifold of functions; fiber integral; diffeomorphism group
Summary:
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].
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