Topological Complexity of Configuration Spaces

Michael Farber*, Mark Grant

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


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 languageEnglish
Pages (from-to)1841-1847
Number of pages8
JournalProceedings of the American Mathematical Society
Issue number5
Early online date29 Dec 2008
Publication statusPublished - May 2009

Bibliographical note

This research was supported by grants from the EPSRC and from The Royal Society


  • topological complexity
  • configuration spaces
  • robot motion


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