On the classifying space of Artin monoids
Abstract
A theorem proved by Dobrinskaya in 2006 shows that there is a strong connection between the $K(\pi,1)$ conjecture for Artin groups and the classifying space of Artin monoids. More recently Ozornova obtained a different proof of Dobrinskaya's theorem based on the application of discrete Morse theory to the standard CW model of the classifying space of an Artin monoid. In Ozornova's work there are hints at some deeper connections between the abovementioned CW model and the Salvetti complex, a CW complex which arises in the combinatorial study of Artin groups. In this work we show that such connections actually exist, and as a consequence we derive yet another proof of Dobrinskaya's theorem.
 Publication:

arXiv eprints
 Pub Date:
 November 2015
 arXiv:
 arXiv:1511.02062
 Bibcode:
 2015arXiv151102062P
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Group Theory;
 20F36 (Primary) 55R35;
 55U10;
 52C35 (Secondary)
 EPrint:
 Communications in Algebra 45 (11), pp. 47404757 (2017)