Stable cohomology of the IA-automorphism group
Moduli and Friends seminar
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Monday 24 June 2024

Erik Lindell (Institut de Mathématiques de Jussieu – Paris Rive Gauche)Stable cohomology of the IA-automorphism group

The group Aut(Fn), where Fn is the free group on n generators, is an object of fundamental interest in low dimensional topology, where it appears as a kind of mapping class group of a wedge of circles. The IA-automorphism group, denoted IAn, is the subgroup of Aut(Fn) consisting of those automorphisms which act as the identity on the abelianization of Fn. From the perspective of low dimensional topology, it is thus an analogue of the Torelli group of a surface. In comparison to Aut(Fn), our understanding of IAn is still very limited. For example, we do not know whether it is finitely presented in general. More generally, we know very little about the (co)homology of IAn, in degrees above one. In this talk I will review recent results concerning the "stable" part of the (co)homology, i.e. the cohomology in degrees small enough compared to the number of generators n.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.