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

Paolini, Giovanni

doi:10.2140/agt.2019.19.3615

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

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

Giovanni Paolini

Algebraic & Geometric Topology 19 (2019) 3615–3639

DOI: 10.2140/agt.2019.19.3615

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

Volume 19, issue 7 (2019)