Configuration spaces of labeled particles and finite Eilenberg-MacLane complexes

被引：0

作者：

Dobrinskaya N.È. ^{[1
]}

机构：

[1] Department of Higher Geometry and Topology, Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow

来源：

Proceedings of the Steklov Institute of Mathematics | 2006年 / 252卷 / 1期

基金：

俄罗斯基础研究基金会;

关键词：

Configuration Space; Orbit Space; Hyperplane Arrangement; Artin Group; Coxeter System;

D O I：

10.1134/S0081543806010056

中图分类号：

学科分类号：

摘要：

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. © Pleiades Publishing, Inc., 2006.

引用

页码：30 / 46

页数：16

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