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 |
Bibliographical note
This research was supported by grants from the EPSRC and from The Royal SocietyFunding
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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