Cubulating a free-product-by-cyclic group

Dahmani, François; Meda Satish, Suraj Krishna

doi:10.2140/agt.2025.25.1561

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Cubulating a free-product-by-cyclic group

François Dahmani and Suraj Krishna Meda Satish

Algebraic & Geometric Topology 25 (2025) 1561–1597

DOI: 10.2140/agt.2025.25.1561

Abstract

Let $G = H_{1} * \dots * H_{k} * F_{r}$ be a finitely generated torsion-free group and $ϕ$ an automorphism of $G$ that preserves this free factor system. We show that when $ϕ$ is fully irreducible and atoroidal relative to this free factor system, the mapping torus $Γ = G ⋊_{ϕ} ℤ$ acts relatively geometrically on a hyperbolic CAT(0) cube complex. This is a generalisation of a result of Hagen and Wise for hyperbolic free-by-cyclic groups.

Keywords

mapping torus, relative cubulation, CAT(0) cube complex, train track, relative hyperbolicity, atoroidal, fully irreducible

Mathematical Subject Classification

Primary: 20E08, 20E36, 20F65, 20F67

References

Publication

Received: 9 April 2023

Revised: 1 December 2023

Accepted: 28 January 2024

Published: 20 June 2025

Authors

François Dahmani
Institut Fourier University Grenoble Alpes Grenoble France

Suraj Krishna Meda Satish
Department of Mathematics Ashoka University Haryana India

Open Access made possible by participating institutions via Subscribe to Open.

Volume 25, issue 3 (2025)