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2019 On the local homology of Artin groups of finite and affine type
Giovanni Paolini
Algebr. Geom. Topol. 19(7): 3615-3639 (2019). 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.

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Giovanni Paolini. "On the local homology of Artin groups of finite and affine type." Algebr. Geom. Topol. 19 (7) 3615 - 3639, 2019. https://doi.org/10.2140/agt.2019.19.3615

Information

Received: 2 July 2018; Revised: 14 January 2019; Accepted: 11 February 2019; Published: 2019
First available in Project Euclid: 3 January 2020

zbMATH: 07162215
MathSciNet: MR4045362
Digital Object Identifier: 10.2140/agt.2019.19.3615

Subjects:
Primary: 05E45, 20F36, 52C35

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.19 • No. 7 • 2019
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