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 $G_k(\mathbb {R}^{n})$ . We use cohomology methods to give estimates on the zero-divisor cup-length of $G_k(\mathbb {R}^{n})$ for various $2\leqslant k< n$ , which in turn give us lower bounds on topological complexity. Our results correct and improve several results from Pavešić (Proc. Roy. Soc. Edinb. A151 (2021), 2013–2029).

Corrigendum to “Topological complexity of real Grassmannians”

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There is a problem with the proofs of [1], Lemma 4.4 and the related Theorems 4.5, 4.8 and 4.12 regarding the computation of zero-divisor cup-length of real Grassmann manifolds G k (R n ). The correct statements and improved estimates of the topological complexity of G k (R n ) will appear in a separate paper by M. Radovanović [2].

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“…The precise formulations include several cases and sub-cases and will be presented in detail in a forthcoming paper by M. Radovanović [2]. We are grateful to Prof. Radovanović who discovered the error and provided corrected and improved estimates.…”