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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

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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:
DateEvent
September 2011Published
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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