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The first homology of $\operatorname{IA}_n$ with coefficients in spaces of Jacobi diagrams

Published 16 Dec 2023 in math.AT, math.GR, and math.QA | (2312.10428v1)

Abstract: The aim of this paper is to compute the first homology of $\operatorname{IA}_n$ with coefficients in the $\operatorname{Aut}(F_n)$-module $A_2(n)$ of Jacobi diagrams of degree $2$ on $n$-component oriented arcs. We also prove the self-duality of the $\operatorname{Aut}(F_3)$-submodule $A''_2(3)$ of $A_2(3)$ which is generated by a certain element.

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