The Dehn function of Richard Thompson's group \(F\) is quadratic.

DOI10.1007/s00222-005-0462-zzbMath1166.20024arXivmath/0211395OpenAlexW2004900196MaRDI QIDQ818633

Victor S. Guba

Publication date: 21 March 2006

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0211395

zbMATH Keywords

isoperimetric functionsDehn functionsThompson group \(F\)

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Topological methods in group theory (57M07)

Related Items (17)

Tamari lattices, forests and Thompson monoids ⋮ R. Thompson’s group and the amenability problem ⋮ Tame filling invariants for groups ⋮ Asymptotic cones of HNN extensions and amalgamated products. ⋮ Compact presentability of tree almost automorphism groups ⋮ Weak commutativity, virtually nilpotent groups, and Dehn functions ⋮ Growth of positive words and lower bounds of the growth rate for Thompson’s groups F(p) ⋮ SOME GROUP THEORY PROBLEMS ⋮ Tame combing and almost convexity conditions. ⋮ Non-commutative arithmetics on Thompson's monoid ⋮ The Dehn function of the generalized Thompson group is quadratic. ⋮ Autostackability of Thompson's group \(F\) ⋮ The homeomorphism problem for closed 3-manifolds ⋮ Divergence functions of Thompson groups ⋮ Conjugacy problem in groups with quadratic Dehn function ⋮ Asymptotic invariants, complexity of groups and related problems ⋮ Diagram groups and directed 2-complexes: homotopy and homology.

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• An infinite-dimensional torsion-free \(\text{FP}_{\infty}\) group
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• Isoperimetric inequalities and the homology of groups
• Introductory notes on Richard Thompson's groups
• On the asymptotic cone of groups satisfying a quadratic isoperimetric inequality
• Diagram groups
• Polynomial upper bounds for the Dehn function of R. Thompson's group F
• Finiteness properties of groups

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