On the Andreadakis equality for a subgroup of the McCool group

2019/02/26 by Abdoulrahim Ibrahim, Ibrahim, Abdoulrahim
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1902.10033

openalex publication_date 2019/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The McCool group has families of subgroups such as the ordinary pure braid group, the upper triangular McCool group and the partial inner automorphism group. The generalized Andreadakis conjecture holds for the ordinary pure braid group and the upper triangular McCool group. In this paper, we prove a similar result for the partial inner automorphism group and also establish an isomorphism between this group and the inner automorphism group of the upper triangular McCool group.

Citations

• On Basis-Conjugating Automorphisms of Free Groups

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