Topological Methods in Nonlinear Analysis

Higher topological complexity of subcomplexes of products of spheres and related polyhedral product spaces

Jesús González, Bárbara Gutiérrez, and Sergey Yuzvinsky

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We construct "higher" motion planners for automated systems whose spaces of states are homotopy equivalent to a polyhedral product space $Z(K,\{(S^{k_i},\star)\})$, 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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Topol. Methods Nonlinear Anal., Volume 48, Number 2 (2016), 419-451.

First available in Project Euclid: 21 December 2016

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González, Jesús; Gutiérrez, Bárbara; Yuzvinsky, Sergey. Higher topological complexity of subcomplexes of products of spheres and related polyhedral product spaces. Topol. Methods Nonlinear Anal. 48 (2016), no. 2, 419--451. doi:10.12775/TMNA.2016.051.

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