Geometry of free extensions of free groups via automorphisms with fixed points on the complex of free factors

Ghosh, Pritam; Gültepe, Funda

doi:10.2140/agt.2025.25.4357

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Geometry of free extensions of free groups via automorphisms with fixed points on the complex of free factors

Pritam Ghosh and Funda Gültepe

Algebraic & Geometric Topology 25 (2025) 4357–4389

DOI: 10.2140/agt.2025.25.4357

Abstract

We give conditions of an extension of a free group to be hyperbolic and relatively hyperbolic using the dynamics of the action of $Out (𝔽)$ on the complex of free factors combined with weak attraction theory. We work with subgroups of exponentially growing outer automorphisms and instead of using a standard ping-pong argument with loxodromics, we allow fixed points for the action and investigate the geometry of the extension group when the fixed points of the automorphisms on the complex of free factors are sufficiently far apart.

Keywords

outer automorphism group of the free group, group extensions, free-by-free groups, complex of free factors

Mathematical Subject Classification

Primary: 20E06, 20F28, 20F67, 57M07

References

Publication

Received: 13 May 2024

Revised: 30 September 2024

Accepted: 3 November 2024

Published: 29 October 2025

Authors

Pritam Ghosh
Department of Mathematics Ashoka University Sonipat India

Funda Gültepe
Department of Mathematics and Statistics University of Toledo Toledo, OH United States

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Volume 25, issue 7 (2025)