Cohomology of polynomial functiors on free groups
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.
Cite this article
Aurélien Djament, Teimuraz Pirashvili, Christine Vespa, Cohomology of polynomial functiors on free groups. Doc. Math. 21 (2016), pp. 205–222DOI 10.4171/DM/531