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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 classification of cohomology transfers for ramified covering maps

Marcelo A. Aguilar, Carlos Prieto (2006)

Fundamenta Mathematicae

We construct a cohomology transfer for n-fold ramified covering maps. Then we define a very general concept of transfer for ramified covering maps and prove a classification theorem for such transfers. This generalizes Roush's classification of transfers for n-fold ordinary covering maps. We characterize those representable cofunctors which admit a family of transfers for ramified covering maps that have two naturality properties, as well as normalization and stability. This is analogous to Roush's...

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...

A note on characteristic classes

Jianwei Zhou (2006)

Czechoslovak Mathematical Journal

This paper studies the relationship between the sections and the Chern or Pontrjagin classes of a vector bundle by the theory of connection. Our results are natural generalizations of the Gauss-Bonnet Theorem.

A note on the cohomology ring of the oriented Grassmann manifolds G ˜ n , 4

Tomáš Rusin (2019)

Archivum Mathematicum

We use known results on the characteristic rank of the canonical 4 –plane bundle over the oriented Grassmann manifold G ˜ n , 4 to compute the generators of the ℤ 2 –cohomology groups H j ( G ˜ n , 4 ) for n = 8 , 9 , 10 , 11 . Drawing from the similarities of these examples with the general description of the cohomology rings of G ˜ n , 3 we conjecture some predictions.

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