Arithmetic properties of the cohomology of Artin groups

• Corrado De Concini ^[1] ; Claudio Procesi ^[1] ; Mario Salvetti ^[2] ; Fabio Stumbo ^[3]
  1. [1] Università "La Sapienza", Italy
  2. [2] Università dell’ Aquila, Italy
  3. [3] Università di Ferrara, Italy

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 28, Nº 4, 1999, págs. 695-717
• Idioma: inglés
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  • In this paper we compute the cohomology of all Artin groups associated to finite Coxeter groups, with coefficients in the following module Rq : let R := Q[q, ] be the ring of rational Laurent polynomials and let Rq be given by the action defined by mapping each standard generator to the multiplication by -q. Case An was already considered in a previous paper where the "cohomology table" has nice elementary arithmetic properties. Here also there are similar (more complicated) arithmetic properties for the infinite series, where the methods of proof are similar. For exceptional cases we used a suitable computer program.