The Walker conjecture for chains in Rd

Michael Farber*, Jean Claude Hausmann, Dirk Schütz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A chain is a configuration in l1.....n of segments of length 1.....n-1 consecutively joined to each other such that the resulting broken line connects two given points at a distance 1n. 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.....n. This result is analogous to the conjecture of K. Walker which concerns the special case d=2. ©

Original languageEnglish
Pages (from-to)283-292
Number of pages10
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number2
StatePublished - Sep 2011
Externally publishedYes


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