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arXiv · 1711.01718

Category and Topological Complexity of the configuration space $F(G\times \mathbb{R}^n,2)$

Cesar A. Ipanaque Zapata
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Abstract

The Lusternik-Schnirelmann category cat and topological complexity TC are related homotopy invariants. The topological complexity TC has applications to the robot motion planning problem. We calculate the Lusternik-Schnirelmann category and topological complexity of the ordered configuration space of two distinct points in the product $G\times\mathbb{R}^n$ and apply the results to the planar and spatial motion of two rigid bodies in $\mathbb{R}^2$ and $\mathbb{R}^3$ respectively.

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Cesar A. Ipanaque Zapata. 2019-04-15. Category and Topological Complexity of the configuration space $F(G\times \mathbb{R}^n,2)$. https://doi.org/10.1017/s0004972719000479

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