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The ℤ₂-cohomology cup-length of real flag manifolds

Július Korbaš, Juraj Lörinc (2003)

Fundamenta Mathematicae

Using fiberings, we determine the cup-length and the Lyusternik-Shnirel’man category for some infinite families of real flag manifolds O ( n + . . . + n q ) / O ( n ) × . . . × O ( n q ) , q ≥ 3. We also give, or describe ways to obtain, interesting estimates for the cup-length of any O ( n + . . . + n q ) / O ( n ) × . . . × O ( n q ) , q ≥ 3. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong’s approach used for calculations in the ℤ₂-cohomology algebra of the Grassmann manifolds.

The computation of Stiefel-Whitney classes

Pierre Guillot (2010)

Annales de l’institut Fourier

The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here “compute” means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet).Next,...

The Euler-Poincaré-Hopf theorem for flat connections in some transitive Lie algebroids

Jan Kubarski (2006)

Czechoslovak Mathematical Journal

This paper is a continuation of [19], [21], [22]. We study flat connections with isolated singularities in some transitive Lie algebroids for which either or s l ( 2 , ) or so ( 3 ) are isotropy Lie algebras. Under the assumption that the dimension of the isotropy Lie algebra is equal to n + 1 , where n is the dimension of the base manifold, we assign to any such isolated singularity a real number called an index. For -Lie algebroids, this index cannot be an integer. We prove the index theorem (the Euler-Poincaré-Hopf...

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