A FINITELY PRESENTED GROUP WITH TWO NON-HOMEOMORPHIC ASYMPTOTIC CONES

DOI10.1142/S021819670700369XzbMath1123.20035arXivmath/0504350OpenAlexW1999511996MaRDI QIDQ5297792

Mark V. Sapir, Alexander Yu. Ol'shanskii

Publication date: 13 July 2007

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504350

zbMATH Keywords

asymptotic conesfinitely generated groupsisoperimetric functionsDehn functions

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Asymptotic properties of groups (20F69) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items

GROUPS WITH QUADRATIC-NON-QUADRATIC DEHN FUNCTIONS, Asymptotic cones of HNN extensions and amalgamated products., Local topological properties of asymptotic cones of groups., The homeomorphism problem for closed 3-manifolds, Lacunary hyperbolic groups. With an appendix by Michael Kapovich and Bruce Kleiner., UNIVERSAL TREE-GRADED SPACES AND ASYMPTOTIC CONES, Asymptotic invariants, complexity of groups and related problems

Cites Work

• Gromov's theorem on groups of polynomial growth and elementary logic
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Higher connectedness of asymptotic cones.
• Asymptotic cones of finitely presented groups
• Tree-graded spaces and asymptotic cones of groups. (With an appendix by Denis Osin and Mark Sapir).
• EXPLICIT CONSTRUCTIONS OF UNIVERSAL ℝ-TREES AND ASYMPTOTIC GEOMETRY OF HYPERBOLIC SPACES
• Asymptotic Cones of Finitely Generated Groups
• QUASI-ISOMETRY INVARIANTS AND ASYMPTOTIC CONES
• GROUPS WITH QUADRATIC-NON-QUADRATIC DEHN FUNCTIONS