Topological complexity of real Grassmannians. Issue 6 (December 2021)

• Record Type: Journal Article
• Authors: Pavešić, Petar
• Is Part Of: Proceedings. Volume 151:Issue 6(2021)
• Page Start: 2013
• Page End: 2029
• Publication Date: 2021-12
• Subjects: Topological complexity -- Lusternik–Schnirelmann category -- Stiefel–Whitney classes -- Grassmann manifold -- zero divisor cup-length; 55M30 -- 55S40; Mathematics -- Periodicals; 510
• DOI: 10.1017/prm.2020.92
• Languages: English
• ISSNs: 0308-2105

Abstract

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 .