The topology of discrete groups

DOI10.1016/0022-4049(80)90040-7zbMath0419.20026OpenAlexW1995344822MaRDI QIDQ1132178

Gilbert Baumslag, Alex Heller, Eldon Dyer

Publication date: 1980

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(80)90040-7

zbMATH Keywords

fundamental groupfinitely generated subgroupsalgebraically closed grouphomotopy groupsintegral homology groupsgeneralized free productgeometrically finite groupacyclic groupcentres of acyclic groupsembedding groups into acyclic groupsfinite, connected, simplicial complexesgeometrically finite dimensionHnn-extensionmitosis of a groupmitotic grouppointed connected Cw-complexsubgroup of an acyclic, geometrically finite group

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Homological methods in group theory (20J05) Other groups related to topology or analysis (20F38) Homotopy theory (55P99) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) Local properties of groups (20E25) Category of groups (20J15) Homology with local coefficients, equivariant cohomology (55N25)

Related Items (47)

Linear representations of binate groups ⋮ NEW INVARIANTS FOR GROUPS ⋮ Surgery obstructions on closed manifolds and the inertia subgroup ⋮ Euler characteristics of 3-manifold groups and discrete subgroups of SL(2, \({\mathbb{C}})\) ⋮ Simplicial complexes triangulating infinite-dimensional manifolds ⋮ Theories of presheaf type ⋮ On the simplicial volume and the Euler characteristic of (aspherical) manifolds ⋮ On cohomology rings of infinite groups. ⋮ Homotopy in Functor Categories ⋮ Groups with no nontrivial linear representations ⋮ A connection between the integral homology and the centre of a rational linear group ⋮ Free and properly discontinuous actions of discrete groups on homotopy circles ⋮ BOUNDED COHOMOLOGY AND BINATE GROUPS ⋮ On one-relator groups which satisfy Poincaré duality ⋮ Nilpotency of Bocksteins, Kropholler's hierarchy and a conjecture of Moore. ⋮ Bounds on Cheeger-Gromov invariants and simplicial complexity of triangulated manifolds ⋮ The acyclic group dichotomy. ⋮ Unnamed Item ⋮ Every finite complex is the classifying space for proper bundles of a virtual Poincaré duality group ⋮ The cohomology of Bestvina-Brady groups. ⋮ Contractible manifolds with exotic positive scalar curvature behavior ⋮ Products of acyclic groups - examples ⋮ On Invariants of Hirzebruch and Cheeger-Gromov ⋮ On a conjecture of Gottlieb ⋮ On higher order homological finiteness of rewriting systems. ⋮ A finitely generated group that does not satisfy the generalized Burghelea Conjecture ⋮ Finite group extensions and the Atiyah conjecture ⋮ Some groups of finite homological type. ⋮ Link concordance and algebraic closure. II ⋮ Homology of some groups of PL-homeomorphisms of the line ⋮ Yang-Mills theory over surfaces and the Atiyah-Segal theorem ⋮ A Topological Approach to Cheeger-Gromov Universal Bounds for von Neumann ρ-Invariants ⋮ Atiyah's \(L^2\)-index theorem, Kan-Thurston construction, and weak Bass conjecture. ⋮ Strongly torsion generated groups from K-theory of real C*-algebras ⋮ Manifolds on Which Only Tori Can Act ⋮ Two functions from Abelian groups to perfect groups ⋮ Multiplicative Invariants and the Finite Co‐Hopfian Property ⋮ Twisted conjugacy and commensurability invariance ⋮ On the integral homology of finitely-presented groups ⋮ Finiteness conditions for groups ⋮ Binate towers of groups ⋮ Free subgroups of certain one-relator groups defined by positive words ⋮ Pseudo-mitotic groups ⋮ Pseudo-mitotic groups. Addendum ⋮ Every finite complex has the homology of some \(\mathrm{CAT}(0)\) cubical duality group ⋮ Every finite complex has the homology of a duality group ⋮ Transfers, Centers, and Group Cohomology

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