### 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 tire topological complexity of the configuration space of n distinct points in Euclidean m-space for all m >= 2 and n >= 2; 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.

Original language | English |
---|---|

Pages (from-to) | 1841-1847 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 137 |

Issue number | 5 |

Early online date | 29 Dec 2008 |

DOIs | |

Publication status | Published - May 2009 |

### Keywords

- topological complexity
- configuration spaces
- robot motion

## Cite this

Farber, M., & Grant, M. (2009). Topological Complexity of Configuration Spaces.

*Proceedings of the American Mathematical Society*,*137*(5), 1841-1847. https://doi.org/10.1090/S0002-9939-08-09808-0