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arXiv · 2610.36302

The Andreadakis conjecture

C. E. Kofinas
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Abstract

For $n\ge2$, let $F_n$ be the free group of rank $n$, and let $\IA(F_n)$ be the group of automorphisms of $F_n$ acting trivially on its abelianization. Two natural filtrations of $\IA(F_n)$ are its lower central series $γ_c(\IA(F_n))$ and the Andreadakis filtration $\mathrm{I}_{c+1}\mathrm{A}(F_n)$, consisting of automorphisms acting trivially on $F_n/γ_{c+1}(F_n)$, $c \geq 1$. Andreadakis conjectured that these filtrations coincide. We disprove this conjecture for every $n\ge3$ and $c\ge4$.

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C. E. Kofinas. 2026-10-26. The Andreadakis conjecture. https://arxiv.org/abs/2610.36302

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