On maximality of the cup-length of flag manifolds

Abstract

We investigate which real flag manifolds of the form $$F(1,\ldots,1,2,\ldots,2,m)$$ have the \({\mathbb Z_2}\)-cup-length equal to the dimension. We obtain a complete classification of such manifolds of the form \({F(1,\ldots,1,2,m)}\) and \({F(1,\ldots,1,2,2,m)}\). Additionally, we provide an infinite family of manifolds \({F(1,\ldots,1,2,\ldots,2,m)}\) which give the negative answer to a question from J. Korbas and J. Lorinc [5].