Topological complexity of real Grassmannians

Abstract

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