Braids, inner automorphisms and the Andreadakis problem
Algebraic Topology
2022-07-19 v2 Group Theory
Geometric Topology
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.
Keywords
Cite
@article{arxiv.2006.04398,
title = {Braids, inner automorphisms and the Andreadakis problem},
author = {Jacques Darné},
journal= {arXiv preprint arXiv:2006.04398},
year = {2022}
}