Czechoslovak Mathematical Journal, Vol. 70, No. 2, pp. 299-310, 2020
On real flag manifolds with cup-length equal to its dimension
Received June 14, 2018. Published online November 18, 2019.
Abstract: We prove that for any positive integers $n_1,n_2,\ldots,n_k$ there exists a real flag manifold $F(1,\ldots,1,n_1,n_2,\ldots,n_k)$ 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.
Keywords: cup-length; flag manifold; Lyusternik-Shnirel'man category