On the naturality of the exterior differential

C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (1) 2008, pp. 1–10
(Received: 2008-02-19 )

Vladimir Goldshtein, Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer Sheva, Israel; email: vladimir@bgumail.bgu.ac.il

Marc Troyanov, Institut de Geometrie, algebre (IGAT), Batiment BCH, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland; email: marc.troyanov@epfl.ch


We give sufficient conditions for the naturality of the exterior differential under Sobolev mappings. In other words we study the validity of the equation \(d\, f^* \alpha = f^*\, d\alpha\) for a smooth form \(\alpha\) and a Sobolev map \(f\).

Nous donnons des conditions suffisantes pour la validité de la naturalité de la différentielle extérieure par rapport à une application dans un espace de Sobolev. Autrement dit, nous étudions la validité de l’équation \(d\, f^* \alpha = f^*\, d\alpha\) pour une forme différentielle lisse \(\alpha\) et une application de Sobolev \(f\).

Keywords: Sobolev mappings, differential forms

AMS Subject Classification: Sobolev spaces and other spaces of ``smooth'' functions; embedding theorems; trace theorems 46E35

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