%0 Journal Article
%T Induced differential forms on manifolds of functions
%A Cornelia Vizman
%J Mathematics
%D 2011
%I arXiv
%X Differential forms on the Fr\'echet manifold 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 associating (p-k)-forms on F(S,M) to p-forms on M (hat pairing with a constant function) and the bar map associating p-forms on F(S,M) to p-forms on M (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians.
%U http://arxiv.org/abs/1111.3889v1