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Free Representations of Outer Automorphism Groups of Free Products via Characteristic Abelian Coverings by Alexis Marchand is a Mathematics article available to read on EtoBox.
What is Free Representations of Outer Automorphism Groups of Free Products via Characteristic Abelian Coverings about?
Given a free product G, we investigate the existence of faithful free representations of the outer automorphism group Out.G/, or in other words of embeddings of Out.G/ into Out.F m / for some m. This is based on work of Bridson and Vogtmann in which they construct embeddings of Out.F n / into Out.F m / for some values of n and m by interpreting Out.F n / as the group of homotopy equivalences of a graph X of genus n, and by lifting homotopy equivalences of X to a characteristic abelian cover of genus m. Our construction for a free product G, using a presentation of Out.G/ due to Fuchs-Rabinovich, is written as an algebraic proof, but it is directly inspired by Bridson and Vogtmann's topological method and can be interpreted as lifting homotopy equivalences of a graph of groups. For instance, we obtain a faithful free representation of Out.G/ when G n , with F d free of rank d and G i finite abelian of order coprime to n 1.
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It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Alexis Marchand
- Publisher
- Walter de Gruyter GmbH
- Published
- 2022
- Language
- EN
- Field
- Mathematics (Physical Sciences)