Linear representations of Aut(F_r) on the homology of representation varieties

2012/10/11 by Yael Algom-Kfir, Algom-Kfir, Yael, Asaf Hadari +1
Mathematics · #20C99 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #msc:20C99

paper · pdf · doi:10.48550/arxiv.1210.3370

arxiv created 2012/10/11 · openalex publication_date 2012/10/11 · arxiv updated 2012/10/15 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28

Abstract

Let G be a compact semisimple linear Lie group. We study the action of Aut(F_r) on the space H_*(G^r;\QQ). We compute the image of this representation and prove that it only depends on the rank of the Lie algebra of G. We show that the kernel of this representation is always the Torrelli subgroup IA_r of Aut(F_r).

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