## Topological complexity of configuration spaces

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

## Abstract:

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.## References

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## Additional Information

**Michael Farber**- Affiliation: Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom
- Email: michael.farber@durham.ac.uk
**Mark Grant**- Affiliation: School of Mathematics, The University of Edinburgh, King’s Buildings, Edinburgh, EH9 3JZ, United Kingdom
- MR Author ID: 794577
- Email: mark.grant@ed.ac.uk
- 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: https://doi.org/10.1090/S0002-9939-08-09808-0
- MathSciNet review: 2470845