On the topological complexity and zero-divisor cup-length of real Grassmannians

Abstract

Topological complexity naturally appears in the motion planning in robotics. In this paper we consider the problem of finding topological complexity of real Grassmann manifolds. We use cohomology methods to give estimates on the zero-divisor cup-length of for various 2 ≤ k, which in turn give us lower bounds on topological complexity. Our results correct and improve several results from Pavešić (Proc. Roy. Soc. Edinb. A 151 (2021), 2013-2029).