On the linearity of the holomorph group of a free group on two generators

2009/05/03 by Fred Cohen, F. R. Cohen, V. Metaftsis +5
Mathematics · #20F28 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #math.GT #msc:20F28

paper · pdf · doi:10.48550/arxiv.0905.0295

arxiv created 2009/05/03 · openalex publication_date 2009/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F_n denote the free group generated by n letters. The purpose of this article is to show that Hol(F₂), the holomorph of the free group on two generators, is linear. Consequently, any split group extension of F₂ by a linear group H is linear. This result gives a large linear subgroup of Aut(F₃). A second application is that the mapping class group for genus one surfaces with two punctures is linear.

Citations

• On Basis-Conjugating Automorphisms of Free Groups

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