On homology torsion growth
Résumé
We prove new vanishing results on the growth of higher torsion homologies for suitable arithmetic lattices, Artin groups and mapping class groups. The growth is understood along Farber sequences, in particular, along residual chains. For principal congruence subgroups, we also obtain strong asymptotic bounds for the torsion growth. As a central tool, we introduce a quantitative homotopical method called effective rebuilding. This constructs small classifying spaces of finite index subgroups, at the same time controlling the complexity of the homotopy. The method easily applies to free abelian groups and then extends recursively to a wide class of residually finite groups.
Fichier principal
ABFG-2021-06-24.pdf (1.3 Mo)
Télécharger le fichier
Fig1.png (237.74 Ko)
Télécharger le fichier
Fig2.png (724.14 Ko)
Télécharger le fichier
Fig3.png (250.63 Ko)
Télécharger le fichier
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|