Abstract
Let G be a compact semisimple linear Lie group. We study the action of \(\text {Aut}(F_r)\) on the space \(H_*(G^r; {\mathbb {Q}})\). We compute the image of this representation and prove that it only depends on the rank of \({\mathfrak {g}}\). We show that the kernel of this representation is always the Torrelli subgroup \(\text {IA}_r\) of \(\text {Aut}(F_r)\).
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Algom-Kfir, Y., Hadari, A. Linear representations of \(\text {Aut}(F_r)\) on the homology of representation varieties. Geom Dedicata 209, 199–206 (2020). https://doi.org/10.1007/s10711-020-00530-w
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DOI: https://doi.org/10.1007/s10711-020-00530-w