Charges in middle dimensions

De Pauw, Thierry;Moonens, Laurent;Pfeffer, Washek F.
(2009) Journal de mathématiques pures et appliquées — Vol. 92, n° 1, p. 86-112 (2009)

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Authors
  • De Pauw, ThierryUCLouvain
    Author
  • Moonens, LaurentUCLouvain
    Author
  • Pfeffer, Washek F.
    Author
Abstract
Giving the space N-m(R-n) of m-dimensional normal currents a suitable topology, we define charges as continuous linear functionals. A continuous differential form omega : R-n -> Lambda R-m(n) acting on N-m(R-n) by <omega, T > := < T, omega > is an example of a charge. We show that for every charge alpha there are continuous m- and (m - 1)-dimensional forms omega and zeta such that alpha = omega + d zeta holds weakly. This representation can be used to define a cohomology akin to that of de Rham. (c) 2009 Elsevier Masson SAS. All rights reserved.
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De Pauw, T., Moonens, L., & Pfeffer, W. F. (2009). Charges in middle dimensions. Journal de mathématiques pures et appliquées, 92(1), 86-112. https://doi.org/10.1016/j.matpur.2009.04.001 (Original work published 2009)