Work

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

Year: 2025

Type: article

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.20E06, 20F28, 20F67, 57M07

Source: Algebraic & Geometric Topology

DOI: 10.2140/agt.2025.25.4357

Authors: Pritam Ghosh, Funda Gültepe

Institutions: Ashoka University, University of Toledo

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Award: LEAPS MPS: Surface subgroups of outer automorphism group of the free group and dynamics on the boundary