## Abstract

A chain is a configuration in l_{1}....._{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 _{1}n. For a fixed generic set of length parameters the space of all chains in R^{d} 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 l_{1}....._{n}. This result is analogous to the conjecture of K. Walker which concerns the special case d=2. ©

Original language | English |
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Pages (from-to) | 283-292 |

Number of pages | 10 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 151 |

Issue number | 2 |

DOIs | |

State | Published - Sep 2011 |

Externally published | Yes |

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