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Topological complexity of configuration spaces
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Farber, Michael and Grant, Mark (2008) Topological complexity of configuration spaces. Proceedings of the American Mathematical Society, Vol.137 (No.5). pp. 1841-1847. doi:10.1090/S0002-9939-08-09808-0 ISSN 0002-9939.
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Official URL: http://dx.doi.org/10.1090/S0002-9939-08-09808-0
Abstract
The topological complexity is a homotopy invariant which reflects the complexity of the problem of constructing a motion planning algorithm in the space , viewed as configuration space of a mechanical system. In this paper we complete the computation of the topological complexity of the configuration space of distinct points in Euclidean -space for all and ; the answer was previously known in the cases and odd. We also give several useful general results concerning sharpness of upper bounds for the topological complexity.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||
Publisher: | American Mathematical Society | ||||
ISSN: | 0002-9939 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.137 | ||||
Number: | No.5 | ||||
Page Range: | pp. 1841-1847 | ||||
DOI: | 10.1090/S0002-9939-08-09808-0 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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