The ${\Bbb Z}_2$-cohomology cup-length of real flag manifolds

Július Korbaš ¹   ; Juraj Lörinc ²

¹ Katedra algebry a teórie čísel Fakulta matematiky, fyziky a informatiky Univerzita Komenského Mlynská dolina SK-842 48 Bratislava 4, Slovakia
² Národná banka Slovenska I. Karvaša 1 SK-813 25 Bratislava 1, Slovakia

Fundamenta Mathematicae, Tome 178 (2003) no. 2, pp. 143-158

Résumé

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.

Détail

DOI : 10.4064/fm178-2-4

Keywords: using fiberings determine cup length lyusternik shnirelman category infinite families real flag manifolds dots times dots times geq describe ways obtain interesting estimates cup length dots times dots times geq present another approach combining method fiberings generalize real flag manifolds stongs approach calculations mathbb cohomology algebra grassmann manifolds