## Topological Methods in Nonlinear Analysis

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

#### Abstract

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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 48, Number 2 (2016), 419-451.

Dates
First available in Project Euclid: 21 December 2016

https://projecteuclid.org/euclid.tmna/1482289222

Digital Object Identifier
doi:10.12775/TMNA.2016.051

Mathematical Reviews number (MathSciNet)
MR3642766

Zentralblatt MATH identifier
06712726

#### Citation

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. https://projecteuclid.org/euclid.tmna/1482289222

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