Rigidity of the free factor complex

2023/06/09 by Mladen Bestvina, Martin R. Bridson, Bestvina, Mladen +1
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2306.05941

openalex publication_date 2023/06/09 · openalex created_date 2023/06/13 · openalex updated_date 2026/07/28

Abstract

We establish the following non-abelian analogue of the Fundamental Theorem of Projective Geometry: the natural map from \rmAut(F_n) to the automorphism group of the free-factor complex AF_n is an isomorphism. We also prove the corresponding theorem for the action of \rmOut(F_n) on the complex of conjugacy classes of free factors.

Related

• Amalgamated Free Products of w-Rigid Factors and Calculation of their Symmetry Groups
• Complexes with free actions by the group of automorphisms of a free group
• On a Subfactor Construction of a Factor Non Anti-Isomorphic to Itself
• A presentation for Aut(F_n)
• The Complex of Non-separating embedded spheres