Djament, Aurélien; Pirashvili, Teimuraz; Vespa, Christine

Cohomologie des foncteurs polynomiaux sur les groupes libres

Doc. Math., J. DMV 21, 205-222 (2016)


Summary: We show that extension groups between two polynomial functors on free groups are the same in the category of all functors and in a subcategory of polynomial functors of bounded degree. The proof relies on functorial properties of the group ring of free groups and its filtration by powers of the augmentation ideal. We give some applications, in particular in term of homological dimension.

Mathematics Subject Classification

18A25, 18G15, 20J15, 18E15, 18G10


catégories de foncteurs , groupes libres , foncteurs polynomiaux , groupes d'extensions