Geodesic
Cohomology of polynomial functiors on free groups
Documenta mathematica, Tome 21 (2016), pp. 205-222
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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.
DOI : 10.4171/dm/531
Classification : 18A25, 18G10, 18G15, 20J15
Mots-clés : catégories de foncteurs, groupes libres, foncteurs polynomiaux, groupes d'extensions 
@article{10_4171_dm_531,
     author = {Teimuraz Pirashvili and Christine Vespa and Aur\'elien Djament},
     title = {Cohomology of polynomial functiors on free groups},
     journal = {Documenta mathematica},
     pages = {205--222},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/531},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/531/}
}
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Teimuraz Pirashvili; Christine Vespa; Aurélien Djament. Cohomology of polynomial functiors on free groups. Documenta mathematica, Tome 21 (2016), pp. 205-222. doi: 10.4171/dm/531

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