The Walker conjecture for chains in ℝd
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 0305-0041Full text not available from this repository.
Official URL: http://dx.doi.org/10.1017/S030500411100020X
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|
|Official Date:||September 2011|
|Page Range:||pp. 283-292|
|Access rights to Published version:||Restricted or Subscription Access|
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