On the stable cohomology of the IA-automorphism groups of free groups
Kazuo Habiro, Mai Katada

TL;DR
This paper investigates the stable rational cohomology of IA-automorphism groups of free groups, combining classical theorems and spectral sequences to propose conjectural algebraic structures and relate to surface Torelli groups.
Contribution
It computes the twisted first cohomology of automorphism groups of free groups and proposes a new conjectural algebraic structure for their stable rational cohomology.
Findings
Computed the twisted first cohomology of Aut(F_n)
Studied the stable rational cohomology of IA_n groups
Proposed conjectural algebraic structures for cohomology
Abstract
Borel's stability and vanishing theorem gives the stable cohomology of with coefficients in algebraic -representations. By combining the Borel theorem with the Hochschild-Serre spectral sequence, we compute the twisted first cohomology of the automorphism group of the free group of rank . We also study the stable rational cohomology of the IA-automorphism group of . We propose a conjectural algebraic structure of the stable rational cohomology of , and consider some relations to known results and conjectures. We also consider a conjectural structure of the stable rational cohomology of the Torelli groups of surfaces.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology
