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 SocietyKeywords
- topological complexity
- configuration spaces
- robot motion