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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.

Vanishing theorems on cohomology associated to hermitian symmetric spaces

Shingo Murakami (1987)

Annales de l'institut Fourier

We consider the cohomoly groups of compact locally Hermitian symmetric spaces with coefficients in the sheaf of germs of holomorphic sections of those vector bundles over the spaces which are defined by canonical automorphic factors. We give a quick survey of the research on these cohomology groups, and then discuss vanishing theorems of the cohomology groups.

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