Braids, inner automorphisms and the Andreadakis problem

2020/06/08 by Darné, Jacques · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2006.04398

Abstract

In this paper, we generalize the tools that were introduced in [Dar19b] in order to study the Andreadakis problem for subgroups of IAn. In particular, we study the behaviour of the Andreadakis problem when we add inner automorphisms to a subgroup of IAn. We notably use this to show that the Andreadakis equality holds for the pure braid group on n strands modulo its center acting on the free group on n-1 generators , that is, for the (pure, based) mapping class group of the n-punctured sphere acting on its fundamental group.

Cited by

• On the abelianization of the special derivation Lie algebras of free Lie algebras

Related

• On the Andreadakis problem for subgroups of IA_n
• On the Andreadakis equality for a subgroup of the McCool group
• Normal subgroups of the braid group and the metaconjecture of Ivanov
• Knot invariants from representations of braids by automorphisms of a free group
• Representing braids by automorphisms