On the local homology of Artin groups of finite and affine type
Abstract
We study the local homology of Artin groups using weighted discrete Morse theory. In all finite and affine cases, we are able to construct Morse matchings of a special type (we call them "precise matchings"). The existence of precise matchings implies that the homology has a squarefree torsion. This property was known for Artin groups of finite type, but not in general for Artin groups of affine type. We also use the constructed matchings to compute the local homology in all exceptional cases, correcting some results in the literature.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 arXiv:
 arXiv:1709.01358
 Bibcode:
 2017arXiv170901358P
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Combinatorics;
 Mathematics  Group Theory
 EPrint:
 Algebr. Geom. Topol. 19 (2019) 36153639