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The Walker conjecture for chains in ℝd
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Farber, Michael, Hausmann, Jean-Claude and Schutz, Dirk (2011) The Walker conjecture for chains in ℝd. Mathematical Proceedings of the Cambridge Philosophical Society, Vol.151 (No.2). pp. 283-292. doi:10.1017/S030500411100020X
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Official URL: http://dx.doi.org/10.1017/S030500411100020X
Abstract
A chain is a configuration in ℝd of segments of length ℓ1, . . ., ℓn−1 consecutively joined to each other such that the resulting broken line connects two given points at a distance ℓn. For a fixed generic set of length parameters the space of all chains in ℝd is a closed smooth manifold of dimension (n − 2)(d − 1) − 1. In this paper we study cohomology algebras of spaces of chains. We give a complete classification of these spaces (up to equivariant diffeomorphism) in terms of linear inequalities of a special kind which are satisfied by the length parameters ℓ1, . . ., ℓn. This result is analogous to the conjecture of K. Walker which concerns the special case d=2.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Mathematical Proceedings of the Cambridge Philosophical Society | ||||
| Publisher: | Cambridge University Press | ||||
| ISSN: | 0305-0041 | ||||
| Official Date: | September 2011 | ||||
| Dates: |
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| Volume: | Vol.151 | ||||
| Number: | No.2 | ||||
| Page Range: | pp. 283-292 | ||||
| DOI: | 10.1017/S030500411100020X | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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