G-CW-surgery and \(K_ 0(\)ZG)

DOI10.1007/BF01173912zbMath0484.57022MaRDI QIDQ1163769

Ted Petrie, Robert Oliver

Publication date: 1982

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173125

zbMATH Keywords

Euler characteristicsBurnside ringBurnside group of a G-spaceconstruction of finite G-complexes with prescribed homotopy type and isotropy structureconstruction of G-homotopy spheres with exotic isotropy structurefiniteness obstructions in the projective class groupG-map between finite G-complexesnon-equivariant homotopy-equivalencerelations between projective class groups and transformation groupsvariation of fixed point sets under quasi-equivalence

Mathematics Subject Classification ID

Homotopy equivalences in algebraic topology (55P10) Finite transformation groups (57S17) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Wall finiteness obstruction for CW-complexes (57Q12)

Related Items

Bak groups and equivariant surgery ⋮ Construction of one-fixed-point actions on spheres of nonsolvable groups. I ⋮ Fixed-point sets of smooth actions on spheres ⋮ Topological invariants of real algebraic actions ⋮ Nontrivial \(\mathcal P(G)\)-matched \(\mathfrak S\)-related pairs for finite gap Oliver groups ⋮ Bak groups and equivariant surgery. II ⋮ Homotopiedarstellungen endlicher Gruppen: Dimensionsfunktionen ⋮ Diffeomorphism classification of finite group actions on disks ⋮ Nonlinear analogs of linear group actions on spheres ⋮ The singular set of group actions on homotopy spheres ⋮ The homotopy type of group actions on homotopy spheres

Cites Work

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• The Burnside ring of a compact Lie group. I
• Fixed point sets of group actions on Euclidean space
• G maps and the projective class group
• G-actions on disks and permutation representations
• Subgroups generating D(ZG)
• A Mayer-Vietoris sequence for class groups
• Equivariant cohomology theories
• Equivariant \(K\)-theory and completion
• 𝐺 surgery. II
• Whitehead torsion
• On Modules of Trivial Cohomology over a Finite Group, II (Finitely Generated Modules)
• Introduction to Algebraic K-Theory. (AM-72)

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