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On real flag manifolds with cup-length equal to its dimension. (English) Zbl 1513.14018

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.

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)
57N65 Algebraic topology of manifolds
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