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On real flag manifolds with cup-length equal to its dimension

Marko Radovanović (2020)

Czechoslovak Mathematical Journal

We prove that for any positive integers n 1 , n 2 , ... , n k there exists a real flag manifold F ( 1 , ... , 1 , n 1 , n 2 , ... , n k ) with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.

On residue formulas for characteristic numbers

Francisco Gómez Ruiz (2009)

Banach Center Publications

We show that coefficients of residue formulas for characteristic numbers associated to a smooth toral action on a manifold can be taken in a quotient field Q ( X , . . . , X r ) . This yields canonical identities over the integers and, reducing modulo two, residue formulas for Stiefel Whitney numbers.

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