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A characterization of harmonic sections and a Liouville theorem

Simão Stelmastchuk (2012)

Archivum Mathematicum

Let P ( M , G ) be a principal fiber bundle and E ( M , N , G , P ) an associated fiber bundle. Our interest is to study the harmonic sections of the projection π E of E into M . Our first purpose is give a characterization of harmonic sections of M into E regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of π E .

A G -minimal model for principal G -bundles

Shrawan Kumar (1982)

Annales de l'institut Fourier

Sullivan associated a uniquely determined D G A | Q to any simply connected simplicial complex E . This algebra (called minimal model) contains the total (and exactly) rational homotopy information of the space E . In case E is the total space of a principal G -bundle, ( G is a compact connected Lie-group) we associate a G -equivariant model U G [ E ] , which is a collection of “ G -homotopic” D G A ’s | R with G -action. U G [ E ] will, in general, be different from the Sullivan’s minimal model of the space E . U G [ E ] contains the total rational...

Cobordisme fibré et approximation d’une sous-variété singulière par des sous-variétés C

André Didierjean (1983)

Annales de l'institut Fourier

Dans cet article, on montre comment le cobordisme d’applications et le cobordisme fibré fournissent les obstructions à des problèmes de lissage topologique de singularités avec un lieu singulier compact. On calcule dans le cas des petites dimensions les groupes de cobordisme fibré. Les résultats connus sur le cobordisme fibré ou sur son image dans le cobordisme d’application permettent le calcul d’un certain nombre de ces obstructions.

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