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Keywords:
cup-length; flag manifold; Lyusternik-Shnirel'man category
cup-length; flag manifold; Lyusternik-Shnirel'man category
Summary:
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.
References:
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