On the local homology of Artin groups of finite and affine type

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 square-free torsion. Such a property was known for Artin groups of finite type, but not in general for those of affine type. We also use the constructed matchings to compute the local homology in all exceptional cases, correcting some results in the literature.