Relative hyperbolicity of free-by-cyclic extensions

2018/02/22 by Pritam Ghosh, Ghosh, Pritam · 6 citations
Mathematics · #20F65 #57M07 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1802.08570

openalex publication_date 2018/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finite rank free group \mathbbF of rank(\mathbbF)≥ 3, we show that the mapping torus of ϕ is (strongly) relatively hyperbolic if ϕ is exponentially growing. We combine our result with the work of Button-Kropholler to answer a question asked by Minasyan-Osin regarding the acylindrical hyperbolicity of such free-by-cyclic extensions. As an application we construct new examples of free-by-free hyperbolic extensions where the elements of the quotient group are not necessarily fully irreducible. We also give a new proof of the Bridson-Groves quadratic isoperimetric inequality theorem.

Cited by

• Largest acylindrical actions of free-by-cyclic groups
• Rank 1 phenomena for 1-relator and deficiency 1 groups
• The geometry of subgroups of mapping tori of free groups
• Relative solidity results and their applications to computations of some II₁ factor invariants
• Finite Index Rigidity of Relatively Hyperbolic Groups
• Characterizing hierarchically hyperbolic free by cyclic groups

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• Relative hyperbolicity of free extensions of free groups
• Relative hyperbolicity of ascending HNN extension of groups
• The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth
• Growth of relatively hyperbolic groups
• Extensions of hyperbolic groups have locally uniform exponential growth