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arXiv · 2006.04398

Braids, inner automorphisms and the Andreadakis problem

Jacques Darné
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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.

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Jacques Darné. 2020-06-08. Braids, inner automorphisms and the Andreadakis problem. https://arxiv.org/abs/2006.04398

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