The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds

Abstract

We compute the rational zero-divisor cup-length of the oriented partial flag manifold F ˜ ( n 1 , … , n k ) \[\widetilde{F}\left( {{n}_{1}},\ldots,{{n}_{k}} \right)\] of type (n 1,…, nk ), k ≥ 2. For certain classes of oriented partial flag manifolds, we compare the rational zero-divisor cup-length and the ℤ 2 \[{{\mathbb{Z}}_{2}}\] -zero-divisor cup-length.