Topological complexity of configuration spaces
Algebraic Topology
2008-06-26 v1
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.
Cite
@article{arxiv.0806.4111,
title = {Topological complexity of configuration spaces},
author = {Michael Farber and Mark Grant},
journal= {arXiv preprint arXiv:0806.4111},
year = {2008}
}