Geodesic
On the local homology of Artin groups of finite and affine type
Paolini, Giovanni1
1 Scuola Normale Superiore, Pisa, Italy
Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3615-3639

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2019.19.3615
Classification : 05E45, 20F36, 52C35
Keywords: Artin groups, discrete Morse theory, homology

Paolini, Giovanni 1

1 Scuola Normale Superiore, Pisa, Italy 
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Paolini, Giovanni. On the local homology of Artin groups of finite and affine type. Algebraic and Geometric Topology, Tome 19 (2019) no. 7, pp. 3615-3639. doi: 10.2140/agt.2019.19.3615

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