Induced differential forms on manifolds of functions
Differential Geometry
2011-11-17 v1
Abstract
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.
Cite
@article{arxiv.1111.3889,
title = {Induced differential forms on manifolds of functions},
author = {Cornelia Vizman},
journal= {arXiv preprint arXiv:1111.3889},
year = {2011}
}
Comments
17 pages