Some computations of stable twisted homology for mapping class groups.

Arthur Soulié (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 University of Glasgow

In this paper, we deal with stable homology computations with twisted coefficients for mapping class groups of surfaces and of 3-manifolds, automorphism groups of free groups with boundaries and automorphism groups of certain right-angled Artin groups. On the one hand, the computations are led using semidirect product structures arising naturally from these groups. On the other hand, we compute the stable homology with twisted coefficients by FI-modules. This notably uses a decomposition result of the stable homology with twisted coefficients for pre-braided monoidal categories proved in this paper.

Domaines: Topologie algébrique [math.AT]; Catégories et ensembles [math.CT]; K-théorie et homologie [math.KT]

Arthur Soulié. Some computations of stable twisted homology for mapping class groups.. Communications in Algebra, 2020, 48 (6), pp.2467-2491. ⟨10.1080/00927872.2020.1716981⟩. ⟨hal-01700031v3⟩