A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups

DOI10.1515/JGT.2006.001zbMath1115.20042arXivmath/0503514MaRDI QIDQ5480154

Peter H. Kropholler

Publication date: 26 July 2006

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503514

zbMATH Keywords

decomposition theoremsgroup extensionsLyndon-Hochschild-Serre spectral sequencesGrothendieck spectral sequencesfundamental groups of graphs of Poincaré duality groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Spectral sequences, hypercohomology (18G40) Cohomology of groups (20J06) Extensions, wreath products, and other compositions of groups (20E22) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06)

Related Items (7)

On complete resolutions ⋮ Groups with Many Finitary Cohomology Functors ⋮ Group cocycles and the ring of affiliated operators ⋮ The geometry of groups containing almost normal subgroups ⋮ Relative Group Cohomology and The Orbit Category ⋮ Modules possessing projective resolutions of finite type ⋮ Complete cohomology for arbitrary rings using injectives

Cites Work

• An infinite-dimensional torsion-free \(\text{FP}_{\infty}\) group
• Splittings of Poincaré duality groups
• Baumslag-Solitar groups and some other groups of cohomological dimension two
• Equivariant Tate-Vogel homology
• Products in negative cohomology
• A homological finiteness criterion
• A remark on subgroups of infinite index in Poincaré duality groups
• Tate cohomology for arbitrary groups via satellites
• Quasi-actions on trees. I: Bounded valence
• The algebraic torus theorem
• Cutting up graphs
• Bounding the complexity of simplicial group actions on trees
• Splitting Groups Over Polycyclic-By-Finite Subgroups

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