Configuration Spaces of Labeled Particles and Finite Eilenberg--MacLane Complexes
Informatics and Automation, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 37-54
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{TRSPY_2006_252_a4,
author = {N. E. Dobrinskaya},
title = {Configuration {Spaces} of {Labeled} {Particles} and {Finite} {Eilenberg--MacLane} {Complexes}},
journal = {Informatics and Automation},
pages = {37--54},
publisher = {mathdoc},
volume = {252},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2006_252_a4/}
}
N. E. Dobrinskaya. Configuration Spaces of Labeled Particles and Finite Eilenberg--MacLane Complexes. Informatics and Automation, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 37-54. http://geodesic.mathdoc.fr/item/TRSPY_2006_252_a4/