Currents relative to a malnormal subgroup system
type: Item
instance of: scholarly article
title: Currents relative to a malnormal subgroup system
author: Yassine Guerch
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2024-11-04T00:00:00Z
review text: Let \(F_{n}\) be a free nonabelian group of rank \(n\). This paper is the first one in a sequence of papers by the author, where he studies the exponential growth of elements of \(\mathrm{Out}(F_{n})\).\N\NIn particular, this paper introduces a new topological space associated with \(F_{n}\) and a malnormal subgroup system \(\mathcal{A}\) of \(F_{n}\), called the space of currents relative to \(\mathcal{A}\), which are \(F_{n}\)-invariant measures on an appropriate subspace of the double boundary of \(F_{n}\). The extension from free factor systems, as considered by \textit{R. Gupta} [Conform. Geom. Dyn. 21, 319--352 (2017; Zbl 1400.20017)] to malnormal subgroup systems is necessary in order to fully study the growth under iteration of outer automorphisms of \(F_{n}\), and requires the introduction of new techniques on cylinders. The author proves that currents associated with elements of \(F_{n}\) that are not contained in a conjugate of a subgroup of \(\mathcal{A}\) are dense in the space of currents relative to \(\mathcal{A}\).
reviewed by: Egle Bettio
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20E08
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 7938075
zbMATH Keywords: nonabelian free group
zbMATH Keywords: outer automorphism group
zbMATH Keywords: space of currents
zbMATH Keywords: group actions on trees
MaRDI profile type: Publication
cites work: Acylindrically hyperbolic groups and their quasi-isometrically embedded subgroups
cites work: Train tracks and automorphisms of free groups
cites work: Q4028720
cites work: Bouts des variétés hyperboliques de dimension 3. (Ends of hyperbolic 3-dimensional manifolds)
cites work: Q5509066
cites work: Relatively hyperbolic groups.
cites work: Q3876158
cites work: ℝ-trees and laminations for free groups III: currents and dual ℝ-tree metrics
cites work: Hyperbolic extensions of free groups
cites work: Length Functions on Currents and Applications to Dynamics and Counting
cites work: The rank of actions on ${R}$-trees
cites work: North-South type dynamics of relative atoroidal automorphisms of free groups on a relative space of currents
cites work: Algebraic laminations for free products and arational trees
cites work: Relative currents
cites work: Subgroup Decomposition in 𝖮𝗎𝗍(𝖥_{𝗇})
cites work: Q5488879
cites work: Geometric intersection number and analogues of the curve complex for free groups.
cites work: On hyperbolicity of free splitting and free factor complexes.
cites work: Counting growth types of automorphisms of free groups.
cites work: Currents, flows and diffeomorphisms
cites work: Quasi-convex groups of isometries of negatively curved spaces
cites work: On the geometry and dynamics of diffeomorphisms of surfaces
cites work: Generalized north-south dynamics on the space of geodesic currents
cites work: Hyperbolic extensions of free groups from atoroidal ping-pong
DOI: 10.5802/AFST.1779
description: scientific article; zbMATH DE number 7938075