${\mathcal{B}$-BOUNDED COHOMOLOGY AND APPLICATIONS

DOI10.1142/S0218196713500057zbMath1285.20053arXiv1004.4677OpenAlexW3098168117MaRDI QIDQ4916251

Crichton Ogle, Ronghui Ji, Bobby W. Ramsey

Publication date: 22 April 2013

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.4677

zbMATH Keywords

cohomology of groupsgrowth conditionsbounded cohomologygroups of polynomial growthDehn functionsrelative hyperbolicitycombable groupsisocohomological groupsweighted complexes

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Cohomology of groups (20J06) (K)-theory and operator algebras (including cyclic theory) (46L80) Hyperbolic groups and nonpositively curved groups (20F67) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18)

Related Items (5)

A spectral sequence for polynomially bounded cohomology ⋮ Polynomially weighted \(\ell^p\)-completions and group homology ⋮ Relative property A and relative amenability for countable groups ⋮ On the Hochschild homology of \(\ell^1\)-rapid decay group algebras ⋮ Bounded homotopy theory and the \(K\)-theory of weighted complexes

Cites Work

• The geometry of the word problem for finitely generated groups.
• Smooth dense subalgebras of reduced group \(C^*\)-algebras, Schwartz cohomology of groups, and cyclic cohomology
• Relative homology and Poincaré duality for group pairs
• Finiteness properties of duality groups
• Polynomially bounded cohomology and discrete groups
• Strict hyperbolization
• Relatively hyperbolic groups, rapid decay algebras, and a generalization of the Bass conjecture
• A spectral sequence for polynomially bounded cohomology
• The isocohomological property, higher Dehn functions, and relatively hyperbolic groups.
• COMBABLE GROUPS HAVE GROUP COHOMOLOGY OF POLYNOMIAL GROWTH
• Characteristic Classes. (AM-76)
• Dehn functions and complexes of groups
• Solvable groups with polynomial Dehn functions
• Finiteness properties of groups
• Straightening and bounded cohomology of hyperbolic groups
• Unnamed Item

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