A note on the characteristic rank and related numbers

Abstract

Abstract This note quantifies, via a sharp inequality, an interplay between (a)the characteristic rank of a vector bundle over a topological space X (b)the ℤ2-Betti numbers of X, and(c)sums of the numbers of certain partitions of integers. In a particular context, (c) is transformed into a sum of the readily calculable Betti numbers of the real Grassmann manifolds.