Robot motion planning, weights of cohomology classes, and cohomology operations

DOI10.1090/S0002-9939-08-09529-4zbMath1151.55004arXiv0706.2497OpenAlexW2963351649MaRDI QIDQ3522336

Mark Grant, Michael S. Farber

Publication date: 1 September 2008

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.2497

zbMATH Keywords

topological complexityLens spacescohomology operationscategory weightweights of cohomology classes

Mathematics Subject Classification ID

Discriminantal varieties and configuration spaces in algebraic topology (55R80) Artificial intelligence for robotics (68T40) Classical topics in algebraic topology (55M99)

Related Items (26)

On the topological complexity of manifolds with abelian fundamental group ⋮ Contiguity distance between simplicial maps ⋮ MOTION PLANNING IN SPACES WITH SMALL FUNDAMENTAL GROUPS ⋮ Topological complexity of symplectic manifolds ⋮ Maps of degree one, LS category and higher topological complexities ⋮ Lusternik-Schnirelmann theory to topological complexity from \(A_{\infty}\)-view point ⋮ Geodesic complexity via fibered decompositions of cut loci ⋮ Different types of topological complexity based on higher homotopic distance ⋮ Topological complexity of \(S^{3}/Q_{8}\) as fibrewise L-S category ⋮ On the topological complexity of aspherical spaces ⋮ Existence results for closed Finsler geodesics via spherical complexities ⋮ Topological complexity of classical configuration spaces and related objects ⋮ Q-topological complexity ⋮ Topological complexity and the homotopy cofibre of the diagonal map ⋮ Pseudo centre and its applications ⋮ Topological complexity, fibrations and symmetry ⋮ On LS-category and topological complexity of some fiber bundles and Dold manifolds ⋮ An upper bound for topological complexity ⋮ Digital topological complexity numbers ⋮ Spherical complexities with applications to closed geodesics ⋮ Symmetric topological complexity of projective and Lens spaces ⋮ Higher topological complexity and its symmetrization ⋮ Topological complexity of configuration spaces ⋮ Unnamed Item ⋮ BIEQUIVARIANT MAPS ON SPHERES AND TOPOLOGICAL COMPLEXITY OF LENS SPACES ⋮ Homotopic distance between maps

Cites Work

• BP-theoretic instabilities to the motion planning problem in 4-torsion lens spaces
• On category weight and its applications
• Topological complexity of motion planning
• Instabilities of robot motion
• Topological robotics in lens spaces
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