Isoperimetric inequalities and the homology of groups

DOI10.1007/BF01244317zbMath0829.20053OpenAlexW2001895313MaRDI QIDQ1319235

Hamish Short, Gilbert Baumslag, Charles F. III Miller

Publication date: 15 January 1996

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

Full work available at URL: https://eudml.org/doc/144136

zbMATH Keywords

complexityfinitely generated groupsfinitely presented groupsfree differential calculusquasi-isometric groupsone relator groupsfree nilpotent groupsHirsch lengthintegral homologymetabelian polycyclic groupsabelianized isoperimetric functionsareas of wordscentralized isoperimetric functionsnumber of relatorstorsion-free one relator groups

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Generators, relations, and presentations of groups (20F05) Generalizations of solvable and nilpotent groups (20F19) Geometric group theory (20F65) Nilpotent groups (20F18) Fundamental group, presentations, free differential calculus (57M05)

Related Items (21)

The Dehn function of Richard Thompson's group \(F\) is quadratic. ⋮ Isoperimetric inequalities for the fundamental groups of torus bundles over the circle ⋮ QUASI-ISOMETRY INVARIANTS AND ASYMPTOTIC CONES ⋮ Fractional isoperimetric inequalities and subgroup distortion ⋮ Polynomially-bounded Dehn functions of groups ⋮ The isoperimetric spectrum of finitely presented groups ⋮ Filling inequalities for nilpotent groups through approximations. ⋮ Geometric presentations of Lie groups and their Dehn functions ⋮ Generalized small cancellation conditions, non-positive curvature and diagrammatic reducibility ⋮ Isoperimetric inequalities for lattices in semisimple Lie groups of rank 2 ⋮ Algorithmically complex residually finite groups ⋮ Cone‐equivalent nilpotent groups with different Dehn functions ⋮ Windings of planar random walks and averaged Dehn function ⋮ The Dehn function of Baumslag's metabelian group. ⋮ Residually free groups do not admit a uniform polynomial isoperimetric function ⋮ Combinatorial methods for detecting surface subgroups in right-angled Artin groups. ⋮ Dehn functions of finitely presented metabelian groups ⋮ On quadratic Dehn functions. ⋮ Uniformly finite homology and amenable groups ⋮ Asymptotic invariants, complexity of groups and related problems ⋮ COMBING NILPOTENT AND POLYCYCLIC GROUPS

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• Free differential calculus. I: Derivation in the free group ring. II: The isomerphism problem of groups. III: Subgroups
• On G-spaces
• The geometry of higman‐neumann‐neumann extensions

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