Homological dimension and Farrel cohomology

DOI10.1016/0021-8693(84)90148-0zbMath0536.20032OpenAlexW2032636648MaRDI QIDQ791659

Bruce M. Ikenaga

Publication date: 1984

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(84)90148-0

zbMATH Keywords

Farrell cohomologyTate cohomologygroups of finite virtual cohomological dimensionacyclic simplicial complexes

Mathematics Subject Classification ID

Homological methods in group theory (20J05)

Related Items (30)

Tate cohomology for arbitrary groups via satellites ⋮ Some aspects of homotopic algebra and non-abelian (co)homology theories ⋮ A Criterion for Projective Modules ⋮ On the finiteness of Gorenstein homological dimensions ⋮ ON ALGEBRAIC INVARIANTS FOR FREE ACTIONS ON HOMOTOPY SPHERES ⋮ Complete cohomological functors on groups ⋮ Injective generation of derived categories and other applications of cohomological invariants of infinite groups ⋮ On certain cohomological invariants of groups. ⋮ Projectively coresolved Gorenstein flat dimension of groups ⋮ New results related to a conjecture of Moore. ⋮ A homological characterization of locally finite groups. ⋮ On certain homological finiteness conditions ⋮ On certain homological invariants of groups. ⋮ Mod \(q\) cohomology and Tate-Vogel cohomology of groups. ⋮ Groups with infinite virtual cohomological dimension which act freely on \(\mathbb{R}{}^ m\times{} S^{n-1}\) ⋮ Groups acting on \(S^ n\times\mathbb{R}^ k\): generalizations of a construction of Hambleton and Pedersen ⋮ On the Gorenstein and cohomological dimension of groups ⋮ On a relation between certain cohomological invariants. ⋮ Equivariant Tate-Vogel homology ⋮ A note on complete resolutions ⋮ On some cohomological invariants for large families of infinite groups ⋮ Complete homology and related dimensions of groups ⋮ On the hierarchy of cohomological dimensions of groups ⋮ Infinite-dimensional homotopy space forms ⋮ (STRONGLY) GORENSTEIN FLAT MODULES OVER GROUP RINGS ⋮ The stable category and invertible modules for infinite groups ⋮ On the zeroeth complete cohomology. ⋮ On groups of type \((FP)_\infty\) ⋮ Transformation groups on \(S^ n\times\mathbb{R}^ m\) ⋮ Generalized cohomological dimension

Cites Work

• On groups with periodic cohomology after 1-step
• On cohomological periodicity for infinite groups
• On virtual properties and group extensions
• An extension of Tate cohomology to a class of infinite groups
• Finiteness conditions for CW-complexes. I, II.
• Les foncteurs dérivés de lim et leurs applications en théorie des modules
• Periodic Projective Resolutions
• Uncountable Locally Finite Groups have One End
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