Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Topological complexity of configuration spaces
HTML articles powered by AMS MathViewer

by Michael Farber and Mark Grant PDF
Proc. Amer. Math. Soc. 137 (2009), 1841-1847 Request permission


The topological complexity $\mathsf {TC}(X)$ 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 $m\ge 2$ and $n\ge 2$; 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.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 55M99, 55R80, 68T40
  • Retrieve articles in all journals with MSC (2000): 55M99, 55R80, 68T40
Additional Information
  • Michael Farber
  • Affiliation: Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom
  • Email:
  • Mark Grant
  • Affiliation: School of Mathematics, The University of Edinburgh, King’s Buildings, Edinburgh, EH9 3JZ, United Kingdom
  • MR Author ID: 794577
  • Email:
  • Received by editor(s): June 25, 2008
  • Published electronically: December 29, 2008
  • Additional Notes: This research was supported by grants from the EPSRC and from The Royal Society
  • Communicated by: Alexander N. Dranishnikov
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 1841-1847
  • MSC (2000): Primary 55M99, 55R80; Secondary 68T40
  • DOI:
  • MathSciNet review: 2470845