On maximality of the cup-length of flag manifolds

Abstract

We investigate which real flag manifolds of the form F(1,…,1,2,…,2,m)have the Z2-cup-length equal to the dimension. We obtain a complete classification of such manifolds of the form F(1 , … , 1 , 2 , m) and F(1 , … , 1 , 2 , 2 , m). Additionally, we provide an infinite family of manifolds F(1 , … , 1 , 2 , … , 2 , m) which give the negative answer to a question from J. Korbaš and J. Lörinc [5].