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Title: A generalization of the exterior product of differential forms combining Hom-valued forms (English)
Author: Gross, Christian
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 38
Issue: 3
Year: 1997
Pages: 587-602
Category: math
Summary: 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. (English)
Keyword: differential forms
Keyword: exterior product
Keyword: multilinear algebra
MSC: 15A75
MSC: 22E30
MSC: 53C05
MSC: 58A05
MSC: 58A10
MSC: 58A15
idZBL: Zbl 0946.58002
idMR: MR1485080
Date available: 2009-01-08T18:36:41Z
Last updated: 2012-04-30
Stable URL:
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Reference: [2] Gross C.: Operators on differential forms for Lie transformation groups.Journal of Lie Theory 6 (1996), 1-17. Zbl 0872.58001, MR 1406002
Reference: [3] Gross C.: Connections on fiber bundles and canonical extensions of differential forms., Preprint No. 1795.
Reference: [4] Gross C.: Cohomology and connections on fiber bundles and applications to field theories.Journal of Mathematical Physics 37 12 (1996), 6375-6394. Zbl 0863.53017, MR 1419176
Reference: [5] Helgason S.: Differential Geometry and Symmetric Spaces.Academic Press, 1962. Zbl 0122.39901, MR 0145455
Reference: [6] Kobayashi S., Nomizu K.: Foundations of Differential Geometry.Vol. I, John Wiley & Sons, 1963. Zbl 0526.53001, MR 1393940


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