The ${\Bbb Z}_2$-cohomology cup-length of real flag manifolds
Volume 178 / 2003
Fundamenta Mathematicae 178 (2003), 143-158
MSC: Primary 57R19; Secondary 55M30, 55R05, 57R20, 57T15.
DOI: 10.4064/fm178-2-4
Abstract
Using fiberings, we determine the cup-length and the Lyusternik–Shnirel'man category for some infinite families of real flag manifolds $O(n_1+\dots+n_q)/ O(n_1)\times\dots\times O(n_q)$, $q\geq 3$. We also give, or describe ways to obtain, interesting estimates for the cup-length of any $O(n_1+\dots+n_q)/O(n_1)\times\dots\times O(n_q)$, $q\geq 3$. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong's approach used for calculations in the ${\mathbb Z}_2$-cohomology algebra of the Grassmann manifolds.
