In a previous paper we have given a complete description of linear liftings of p-forms on n-dimensional manifolds M to q-forms on , where is a Weil functor, for all non-negative integers n, p and q, except the case p = n and q = 0. We now establish formulas connecting such liftings and the exterior derivative of forms. These formulas contain a boundary operator, which enables us to define a homology of the Weil algebra A. We next study the case p = n and q = 0 under the condition that A is acyclic. Finally, we compute the kernels and the images of the boundary operators for the Weil algebras and show that these algebras are acyclic.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-3-7,
author = {Jacek D\k ebecki},
title = {Liftings of forms to Weil bundles and the exterior derivative},
journal = {Annales Polonici Mathematici},
volume = {95},
year = {2009},
pages = {289-300},
zbl = {1163.58002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-3-7}
}
Jacek Dębecki. Liftings of forms to Weil bundles and the exterior derivative. Annales Polonici Mathematici, Tome 95 (2009) pp. 289-300. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-3-7/