The Farrell-Tate and Bredon homology for PSL_4(Z) and other arithmetic groups

Abstract : We provide some new computations of Farrell–Tate and Bredon (co)homology for arithmetic groups. For calculations of Farrell-Tate or Bredon homology, one needs cell complexes where cell stabilizers fix their cells pointwise. We provide an algorithm computing an efficient subdivision of a complex to achieve this rigidity property. Applying this algorithm to available cell complexes for PSL_4(Z) and PGL_3(Z[i]) provides computations of Farrell-Tate cohomology for small primes as well as the Bredon homology for the classifying spaces of proper actions with coefficients in the complex representation ring. On the other hand, in order to check correctness of the computer calculations, we describe the Farrell-Tate cohomology in some rank-one cases, using Brown's complex and a number-theoretic description of the conjugacy classification of cyclic subgroups.
Type de document :
Pré-publication, Document de travail
2016
Liste complète des métadonnées

Littérature citée [14 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01398162
Contributeur : Alexander Rahm <>
Soumis le : mercredi 16 novembre 2016 - 17:48:24
Dernière modification le : samedi 19 novembre 2016 - 01:01:48
Document(s) archivé(s) le : jeudi 16 mars 2017 - 15:33:46

Fichiers

FarellAndBredonHomologyOfPSL4Z...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01398162, version 1
  • ARXIV : 1611.06099

Collections

Citation

Anh Tuan Bui, Alexander Rahm, Matthias Wendt. The Farrell-Tate and Bredon homology for PSL_4(Z) and other arithmetic groups. 2016. 〈hal-01398162〉

Partager

Métriques

Consultations de
la notice

38

Téléchargements du document

27