Let F n be the free group on n generators. Consider the group IA n of automorphisms of F n acting trivially on its abelianization. There are two canonical filtrations on IA n : the first one is its lower central series Γ * ; the second one is the Andreadakis filtration A * , defined from the action on F n . In this paper, we establish that the canonical morphism between the associated graded Lie rings L(Γ * ) and L(A * ) is stably surjective. We then investigate a p-restricted version of the Andreadakis problem. A calculation of the Lie algebra of the classical congruence group is also included. arXiv:1711.05991v2 [math.AT]
Let F n be the free group on n generators. Consider the group IA n of automorphisms of F n acting trivially on its abelianization. There are two canonical filtrations on IA n : the first one is its lower central series Γ * ; the second one is the Andreadakis filtration A * , defined from the action on F n . The Andreadakis problem consists in understanding the difference between these filtrations. Here, we show that they coincide when restricted to the subgroup of triangular automorphisms, and to the pure braid group.
Let $F_n$ be the free group on $n$ generators. Consider the group $IA_n$ of automorphisms of $F_n$ acting trivially on its abelianization. There are two canonical filtrations on $IA_n$: the 1st one is its lower central series $\Gamma _*$; the 2nd one is the Andreadakis filtration $\mathcal A_*$, defined from the action on $F_n$. The Andreadakis problem consists in understanding the difference between these filtrations. Here, we show that they coincide when restricted to the subgroup of triangular automorphisms and to the pure braid group.
Our aim here is to showcase several techniques for studying the lower central series of a group and, in particular, for determining whether or not it stops. We apply these techniques to various groups related to braid groups, in particular Artin groups, surface braid groups, groups of welded and virtual braids and partitioned versions of all of these groups.
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