Operations on the A-theoretic nil-terms

DOI10.1112/jtopol/jtm012zbMath1145.19001arXivmath/0702580OpenAlexW1645862864MaRDI QIDQ3507693

John R. Klein, Joachim Grunewald, Tibor Macko

Publication date: 20 June 2008

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

Full work available at URL: https://arxiv.org/abs/math/0702580

zbMATH Keywords

nil groupsalgebraic K-theory of spacesnon-finiteness

Mathematics Subject Classification ID

Stable homotopy theory, spectra (55P42) (K)-theory and homology; cyclic homology and cohomology (19D55) Equivariant homotopy theory in algebraic topology (55P91) Algebraic (K)-theory of spaces (19D10) Negative (K)-theory, NK and Nil (19D35)

Related Items

Segal operations in the algebraic \(K\)-theory of topological spaces ⋮ Teichmüller spaces and negatively curved fiber bundles ⋮ Diffeomorphisms of discs ⋮ Finiteness properties of automorphism spaces of manifolds with finite fundamental group ⋮ The space of Anosov diffeomorphisms ⋮ On the Farrell-Jones conjecture for Waldhausen's \(A\)-theory ⋮ On the topology of the space of pinched negatively curved metrics with finite volume and identical ends ⋮ On the Whitehead Spectrum of the Circle

Cites Work

• The local structure of algebraic K-theory
• The fiber of the linearization map \(A(*) \to K(\mathbb{Z})\)
• Two-primary algebraic \(K\)-theory of pointed spaces
• Stable pseudoisotopy spaces of compact nonpositively curved manifolds
• Relative \(K\)-theory and topological cyclic homology
• The smooth Whitehead spectrum of a point at odd regular primes
• Calculus. I: The first derivative of pseudoisotopy theory
• Categories and cohomology theories
• The groups \(N^ rK_ 0(\mathbb{Z}\pi )\) are finitely generated \(\mathbb{Z} [\mathbb{N}^ r\)-modules if \(\pi\) is a finite group]
• $p$-primary components of homotopy groups I. Exact sequences in Steenrod algebra
• The Nonfiniteness of Nil
• Smash products and Γ-spaces
• The ``fundamental theorem for the algebraic \(K\)-theory of spaces. I
• The ``fundamental theorem for the algebraic \(K\)-theory of spaces. II: The canonical involution

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