Title :

On the stable Andreadakis problem

Author(s) :

Darné, Jacques [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Automorphisms of free groups
Johnson homomorphism

HAL domain(s) :

Mathématiques [math]/Topologie algébrique [math.AT]
Mathématiques [math]/Théorie des groupes [math.GR]

English abstract : [en]

Let $F_n$ be the free group on $n$ generators. Consider the group $IA_n$ of automorpisms of $F_n$ acting trivially on its abelianization. There are two canonical filtrations on $IA_n$: the first one is its lower central ...
Show more >Let $F_n$ be the free group on $n$ generators. Consider the group $IA_n$ of automorpisms of $F_n$ acting trivially on its abelianization. There are two canonical filtrations on $IA_n$: the first one is its lower central series $\Gamma_*$; the second one is the Andreadakis filtration $\mathcal A_*$, defined from the action on $F_n$. In this paper, we establish that the canonical morphism between the associated graded Lie rings ${\mathcal L}(\Gamma_*)$ and ${\mathcal L}(\mathcal A_*)$ 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.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL