The geometry of subgroups of mapping tori of free groups

2025/10/03 by Linton, Marco · 3 citations
#20E07 #20E08 (Secondary) #20F67 (Primary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2510.03145

Abstract

We show that finitely generated mapping tori of free groups have a canonical collection of maximal sub-mapping tori of finitely generated free groups with respect to which they are relatively hyperbolic and locally relatively quasi-convex. As a consequence, we characterise locally quasi-convex hyperbolic groups amongst free-by-cyclic and one-relator groups. We also upgrade several known results for mapping tori of finitely generated free groups to the general case, such as the computations of Dehn functions, the solution to the conjugacy problem and the characterisation of the finitely generated intersection property.

Citations

• The theory of one-relator groups: history and recent progress
• On the cohomological dimension of kernels of maps to \mathbb Z
• On the coherence of one-relator groups and their group algebras
• Virtually free-by-cyclic groups
• On subgroup separability of free-by-cyclic and deficiency 1 groups
• Rational curvature invariants for 2-complexes
• The Conjugacy Problem for ascending HNN-extensions of free groups
• Detecting Relatively Quasiconvex Subgroups and Their Induced Peripheral Structure
• One-relator hierarchies
• Failure of the finitely generated intersection property for ascending HNN extensions of free groups
• Uniform negative immersions and the coherence of one-relator groups
• Negative immersions for one-relator groups
• Relative hyperbolicity of free-by-cyclic extensions
• On distortion of normal subgroups
• Hyperbolic hydra
• The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth
• The quadratic isoperimetric inequality for mapping tori of free group automorphisms
• Groups with small Dehn functions and bipartite chord diagrams
• Coherence, local quasiconvexity, and the perimeter of 2-complexes
• Hyperbolic automorphisms of free groups

Cited by

• Largest acylindrical actions of free-by-cyclic groups
• Embeddings of mapping tori for end-periodic graph maps
• Embedding finitely generated free-by-cyclic groups in finitely generated free-by-cyclic groups

Related

• Embedding finitely generated free-by-cyclic groups in finitely generated free-by-cyclic groups
• The mapping-torus of a free group automorphism is hyperbolic relative to the canonical subgroups of polynomial growth
• Free products of abelian groups in mapping class groups
• Hyperbolic automorphisms of free groups
• Relative hyperbolicity of free extensions of free groups