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The Andreadakis conjecture
Abstract
For n≥2, let Fn be the free group of rank n, and let IA(Fn) be the group of automorphisms of Fn acting trivially on its abelianization. Two natural filtrations of IA(Fn) are its lower central series γc(IA(Fn)) and the Andreadakis filtration Ic+1A(Fn), consisting of automorphisms acting trivially on Fn/γc+1(Fn), c ≥ 1. Andreadakis conjectured that these filtrations coincide. We disprove this conjecture for every n≥3 and c≥4.
Related
BibTeX
@misc{kofinas2026andreadakis,
title = {{The Andreadakis conjecture}},
author = {C. E. Kofinas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36302},
eprint = {2610.36302},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36302},
}
RIS
TY - UNPB
TI - The Andreadakis conjecture
AU - C. E. Kofinas
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36302
UR - https://arxiv.org/abs/2610.36302
AB - For n≥2, 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 I_c+1A(F_n), consisting of automorphisms acting trivially on F_n/γ_c+1(F_n), c ≥ 1. Andreadakis conjectured that these filtrations coincide. We disprove this conjecture for every n≥3 and c≥4.
ER -