The higher topological complexity of subcomplexes of products of spheres---and related polyhedral product spaces

2015/01/29 by Jesús González, González, Jesús, Bárbara Gutiérrez +3 · 1 citation
Computer Science · Engineering · Mathematics · #20F36 #52B70 #52C35 #55M30 #55U10 #68T40 #Algebraic Topology (math.AT) #Digital Image Processing Techniques #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Robotic Mechanisms and Dynamics #math.AT #msc:20F36 #msc:52B70 #msc:52C35 #msc:55M30 #msc:55U10 #msc:68T40

paper · pdf · doi:10.48550/arxiv.1501.07474

30 pages. This second version of the paper extends the results of the first version to the case of polyhedral product spaces $Z(K,\{(S^{k_i},\star)\})$ where no restriction is assumed on the sphere dimensions $k_i$

openalex publication_date 2015/01/29 · arxiv created 2015/03/26 · arxiv updated 2015/03/27 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We construct "higher" motion planners for automated systems whose space of states are homotopy equivalent to a polyhedral product space Z(K,\(S^k_i,⋆)\), e.g. robot arms with restrictions on the possible combinations of simultaneously moving nodes. Our construction is shown to be optimal by explicit cohomology calculations. The higher topological complexity of other families of polyhedral product spaces is also determined.

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