Homology and Cell Structure of Nilpotent Spaces

DOI10.2307/2000312zbMath0574.55011OpenAlexW4233983968MaRDI QIDQ3694276

Robert H. Lewis

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/2000312

zbMATH Keywords

Euler characteristichomology decompositionfinitely generated nilpotent grouphomology equivalencecohomologically trivialfinitely dominated nilpotent CW complexesnilpotent complexes of minimal dimension

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Nilpotent groups (20F18) Homotopy theory (55P99) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Cites Work

• Modules over finite groups
• Periodic resolutions for finite groups
• Induced representations and projective modules
• A counterexample to a conjecture of Steenrod
• Euler characteristics of discrete groups and G-spaces
• Wall's obstruction for nilpotent spaces
• Finitely dominated nilpotent spaces
• The vanishing of certain homology and cohomology groups
• Homotopy dimension and simple cohomological dimension of spaces
• Groups with cyclic Sylow subgroups and finiteness conditions for certain complexes
• The finiteness obstructions for nilpotent spaces lie in \(D(Z\pi)\)
• Homology and central series of groups
• Finiteness conditions for CW-complexes. I, II.
• A cohomological characterization of finite nilpotent groups
• The Grothendieck ring of a finite group
• The geometric realization of Wall obstructions by nilpotent and simple spaces
• Equivariant Cofibrations and Nilpotency
• Vanishing Homology over Nilpotent Groups
• The obstruction to the finiteness of the total space of a fibration

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