Deficiency and abelianized deficiency of some virtually free groups

DOI10.1017/S030500410700045XzbMath1131.20020arXivmath/0607671MaRDI QIDQ5428375

Martin R. Bridson, Michael Tweedale

Publication date: 22 November 2007

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607671

zbMATH Keywords

HNN extensionsnumbers of generatorsfinite presentationsdeficienciesrelation gaps

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Topological methods in group theory (57M07) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06)

Related Items (13)

Normal generation and \(\ell^2\)-Betti numbers of groups. ⋮ Quillen's plus construction and the D(2) problem ⋮ Rank and deficiency gradients of generalized Thompson groups of type F ⋮ Minimal algebraic complexes over \(D_{4n}\) ⋮ Explicit generators for the relation module in the example of Gruenberg–Linnell ⋮ Generation gaps and abelianized defects of free products ⋮ Homology roses and the D(2)-problem ⋮ An exotic presentation of \(Q_{28}\) ⋮ Constructing presentations of subgroups of right-angled Artin groups. ⋮ Volume gradients and homology in towers of residually-free groups ⋮ On the number of relations in free products of Abelian groups. ⋮ Two remarks on Wall's D2 problem ⋮ Computing fundamental groups from point clouds

Cites Work

• Caractéristiques d'Euler et groupes fondamentaux des variétés de dimension 4
• On locally indicable groups
• Morse theory and finiteness properties of groups
• Minimal resolutions for finite groups
• Finiteness conditions for CW-complexes. I, II.
• Non-efficient torsion-free groups exist
• Bestvina–Brady groups and the plus construction
• FINITE PRESENTATIONS OF GROUPS AND 3-MANIFOLDS

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