Topological complexity of real Grassmannians

Abstract

We use some detailed knowledge of the cohomology ring of real Grassmann manifolds G k (R n ) to compute zero-divisor cup-length and estimate topological complexity of motion planning for k-linear subspaces in R n . In addition, we obtain results about monotonicity of Lusternik-Schnirelmann category and topological complexity of G k (R n ) as a function of n.