Geodesic
A generalization of the exterior product of differential forms combining Hom-valued forms
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 587-602.

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This article deals with vector valued differential forms on $C^\infty$-manifolds. As a generalization of the exterior product, we introduce an operator that combines $\operatorname{Hom}(\bigotimes^s(W),Z)$-valued forms with $\operatorname{Hom}(\bigotimes^s(V),W)$-valued forms. We discuss the main properties of this operator such as (multi)linearity, associativity and its behavior under pullbacks, push-outs, exterior differentiation of forms, etc. Finally we present applications for Lie groups and fiber bundles.
Classification : 15A75, 22E30, 53C05, 58A05, 58A10, 58A15
Keywords: differential forms; exterior product; multilinear algebra 
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     author = {Gross, Christian},
     title = {A generalization of the exterior product of differential forms combining {Hom-valued} forms},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {587--602},
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     volume = {38},
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     zbl = {0946.58002},
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     url = {http://geodesic.mathdoc.fr/item/CMUC_1997__38_3_a15/}
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Gross, Christian. A generalization of the exterior product of differential forms combining Hom-valued forms. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 587-602. http://geodesic.mathdoc.fr/item/CMUC_1997__38_3_a15/