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arXiv · 0806.4111

Topological complexity of configuration spaces

Michael Farber·Mark Grant
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Abstract

The topological complexity TC(X) is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space X, viewed as configuration space of a mechanical system. In this paper we complete the computation of the topological complexity of the configuration space of n distinct points in Euclidean m-space for all m>1$ and n>1; the answer was previously known in the cases m=2 and m odd. We also give several useful general results concerning sharpness of upper bounds for the topological complexity.

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Michael Farber, Mark Grant. 2008-06-25. Topological complexity of configuration spaces. https://arxiv.org/abs/0806.4111

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