Charges in middle dimensions

被引：16

作者：

De Pauw, Thierry ^{[1
]}

Moonens, Laurent ^{[2
]}

Pfeffer, Washek F. ^{[3
]}

机构：

[1] Univ Denis Diderot Paris 7, Inst Math Jussieu, Equipe Geometrie & Dynam, F-75205 Paris 13, France

[2] Univ Catholique Louvain, Dept Math, B-1348 Louvain, Belgium

[3] Univ Calif Davis, Dept Math, Davis, CA 95616 USA

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2009年 / 92卷 / 01期

关键词：

Localized locally convex topologies; Normal currents; Representation of charges and flat cochains; Cohomology;

D O I：

10.1016/j.matpur.2009.04.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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(m)R(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.

引用

页码：86 / 112

页数：27

共 13 条

[1]

Bourgain J, 2003, J AM MATH SOC, V16, P393

[2]

De Pauw T, 1998, INDIANA U MATH J, V47, P99

[3] On the exceptional sets of the flux of a bounded vectorfield [J].

De Pauw, T .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2003, 82 (09) :1191-1217

[4] Distributions for which div υ = F has a continuous solution [J].

De Pauw, Thierry ;

Pfeffer, Washek F. .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2008, 61 (02) :230-260

[5]

Edwards R.E., 1995, FUNCTIONAL ANAL

[6]

Evans L. C., 2018, Studies in Advanced Mathematics

[7]

Federer H., 1969, GEOMETRIC MEASURE TH, V153

[8]

MOONENS L, CAND MATH B IN PRESS

[9] The multidimensional Luzin theorem [J].

Moonens, Laurent ;

Pfeffer, Washek F. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 339 (01) :746-752

[10]

Oxtoby J. C., 1971, MEASURE CATEGORY

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