This article is cited in 10 papers

Configuration Spaces of Labeled Particles and Finite Eilenberg–MacLane Complexes

N. E. Dobrinskaya

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: For any Coxeter system $(W,S)$, the group $W$ acts naturally on the complement of the associated complex hyperplane arrangement. By the well-known conjecture, the orbit space of this action is the classifying space of the corresponding Artin group. We describe some properties of configuration spaces of particles labeled by elements of a partial monoid and use them to prove that the orbit space mentioned in the conjecture is the classifying space of the positive Artin monoid. In particular, the conjecture reduces to a problem concerning the group completion of this monoid.

UDC: 515.14

Received in April 2005

 English version: Proceedings of the Steklov Institute of Mathematics, 2006, 252, 30–46

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