The geometry of generalized loxodromic elements

DOI10.5802/AIF.3379OpenAlexW3154147749MaRDI QIDQ2027746

Carolyn R. Abbott, David Hume

Publication date: 28 May 2021

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.03089

zbMATH Keywords

hyperbolicityacylindrical hyperbolicitysmall cancellation

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Cancellation theory of groups; application of van Kampen diagrams (20F06)

Cites Work

• Quasi-convexity of hyperbolically embedded subgroups
• Small cancellation in acylindrically hyperbolic groups
• Constructing group actions on quasi-trees and applications to mapping class groups
• Continuously many quasiisometry classes of \(2\)-generator groups
• Characterizations of Morse quasi-geodesics via superlinear divergence and sublinear contraction
• Bounded cohomology of subgroups of mapping class groups
• Negative curvature in graphical small cancellation groups
• Small cancellation theory over Burnside groups
• Bounded cohomology and isometry groups of hyperbolic spaces
• Tight geodesics in the curve complex
• Acylindrically hyperbolic groups
• Not all finitely generated groups have universal acylindrical actions
• Infinitely presentedC(6)-groups are SQ-universal
• Infinitely presented graphical small cancellation groups are acylindrically hyperbolic
• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
• Largest acylindrical actions and Stability in hierarchically hyperbolic groups

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