I need to learn the Johnson Filtration, which I believe is defined on the automorphism group of free groups. Can anyone recommend some reference to this topic? I know one paper called "On the automorphisms of free groups and free nilpotent groups" by S. Andreadakis, but I am not sure if it is the best or "standard" one to start with.
2026-05-05 18:40:18.1778006418
Reference Request: Johnson Filtration
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There are several papers by Takao Satoh dealing with the Johnson filtration of ${\rm Aut}(F_n)$, which is a descending filtration $$ {\rm Aut}(F_n)={\cal A}_n(0)\supseteq {\cal A}_n(1)\supseteq {\cal A}_n(2)\supseteq \cdots $$ with certain groups of automorphisms of $F_n$. The Johnson filtration of ${\rm Aut}(F_n)$ was originally introduced in $1965$ by Andreadakis, which you know already. It is certainly a good starting point.