Hodge decomposition for stable homology of automorphism groups of free groups

Abstract

We establish a decomposition of stable homology of automorphism groups of free groups with polynomial contravariant coefficients in term of functor homology. This allows several explicit computations, intersecting results obtained by independent methods by O. Randal-Williams and extending some of them.Our methods rely on the investigation of Kan extensions associated to several categories of free groups, the extension of a cancellation criterium for homology with polynomial coefficients due to Scorichenko, Galatius Theorem identifying the stable homology of automorphism groups of free groups to the one of symmetric groups, the machinery of Gamma-spaces and the Snaith splitting.

56 pages, in French

References in corpus (8)

• Cohomological Aspects of Magnus Expansions
• Homology stability for outer automorphism groups of free groups
• Stabilization for the automorphisms of free groups with boundaries
• Erratum to: Homology stability for outer automorphism groups of free groups
• Extension between functors from groups
• Erratum to ``Stabilization for the automorphisms of free groups with boundaries''
• Cohomologie des foncteurs polynomiaux sur les groupes libres
• The stable cohomology of automorphisms of free groups with coefficients in the homology representation

Cited by in corpus (1)

• Extension between functors from groups