Topological Complexity of Configuration Spaces

  • Michael Farber*
  • , Mark Grant
  • *Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)1841-1847
Number of pages8
JournalProceedings of the American Mathematical Society
Volume137
Issue number5
Early online date29 Dec 2008
DOIs
Publication statusPublished - May 2009

Bibliographical note

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

Funding

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

Keywords

  • topological complexity
  • configuration spaces
  • robot motion

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