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. ISSN 0305-0041

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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
Volume:	Vol.151
Number:	No.2
Page Range:	pp. 283-292
Identification Number:	10.1017/S030500411100020X
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/43440

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