Volume 19, issue 7 (2019)

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

Giovanni Paolini

Algebraic & Geometric Topology 19 (2019) 3615–3639
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.

Keywords
Artin groups, discrete Morse theory, homology
Mathematical Subject Classification 2010
Primary: 05E45, 20F36, 52C35
References
Publication
Received: 2 July 2018
Revised: 14 January 2019
Accepted: 11 February 2019
Published: 17 December 2019
Authors
Giovanni Paolini
Scuola Normale Superiore
Pisa
Italy