2024/12/05 by Harry Iveson, Iveson, Harry
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2412.04250
openalex publication_date 2024/12/05 · openalex created_date 2024/12/07 · openalex updated_date 2026/07/28
We give a concise presentation for the outer automorphism group of a free product with no free rank, whose factors are non-trivial, freely indecomposable, not infinite cyclic, and pairwise non-isomorphic. This is achieved by considering the action of the outer automorphism group on a particular subcomplex of `Outer Space', which we show to be simply connected. We then apply a theorem of K. S. Brown to extract our presentation.