Algebraic v. Topological K-Theory: A Friendly Match

DOI10.1007/978-3-642-15708-0_3zbMath1216.19002arXiv0903.3983OpenAlexW1547567735MaRDI QIDQ2996276

Guillermo Cortiñas

Publication date: 6 May 2011

Published in: Topics in Algebraic and Topological K-Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.3983

zbMATH Keywords

Karoubi-Villamayor \(K\)-theoryBott periodicity for \(C^*\)-algebrasQuillen's higher \(K\)-theorytopological \(K\)-theory of Banach algebras

Mathematics Subject Classification ID

Topological (K)-theory (55N15) Topological (K)-theory (19L99) Research exposition (monographs, survey articles) pertaining to algebraic topology (55-02) Research exposition (monographs, survey articles) pertaining to (K)-theory (19-02)

Related Items (13)

Bivariant Hermitian \(K\)-theory and Karoubi's fundamental theorem ⋮ Non-commutative Chern numbers for generic aperiodic discrete systems ⋮ Lifting graph C∗$C^*$‐algebra maps to Leavitt path algebra maps ⋮ Classifying Leavitt path algebras up to involution preserving homotopy ⋮ Algebraic \(k\,k\)-theory and the KH-isomorphism conjecture ⋮ Universal bivariant algebraic \(K\)-theories ⋮ Graded \(K\)-theory, filtered \(K\)-theory and the classification of graph algebras ⋮ Isomorphism conjectures with proper coefficients ⋮ Homotopy invariance through small stabilizations ⋮ Symmetric monoidal noncommutative spectra, strongly self-absorbing \(C^*\)-algebras, and bivariant homology ⋮ Cyclic homology, tight crossed products, and small stabilizations ⋮ Homotopy classification of Leavitt path algebras ⋮ The clean property is not a Morita invariant.

Cites Work

• Relative algebraic K-theory and cyclic homology
• Excision in cyclic homology and in rational algebraic K-theory
• Localization of the K-theory of polynomial extensions
• Algebraic \(K\)-theory and locally convex algebras
• Cyclic homology, derivations, and the free loopspace
• Algebraic \(K\)-theory of stable \(C^*\)-algebras
• Caractère multiplicatif d'un module de Fredholm. (Multiplicative character of a Fredholm module)
• Nilpotence and K-theory
• Excision in bivariant periodic cyclic cohomology
• Bivariant \(K\)-theory for locally convex algebras and the Chern-Connes character
• Delooping classifying spaces in algebraic K-theory
• Excision in bivariant periodic cyclic cohomology: A categorical approach
• Comparison between algebraic and topological \(K\)-theory of locally convex algebras
• The obstruction to excision in \(K\)-theory and in cyclic homology
• Bivariant \(K\)-theory and the Weyl algebra
• Homotopy limits, completions and localizations
• Higher Algebraic K-Theory (After Quillen, Thomason and Others)
• Nil K-Theory Maps to Cyclic Homology
• K-THEORY FOR FRÉCHET ALGEBRAS
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• $K$-théorie algébrique et représentations de groupes
• Cyclic Homology and Nonsingularity
• Bivariant algebraic K-theory
• $K$-théorie algébrique et $K$-théorie topologique I.
• Introduction to Algebraic K-Theory. (AM-72)
• Factorization in Fréchet Modules
• Higher Torsion in H-Spaces
• Excision in algebraic \(K\)-theory
• Simplicial homotopy theory
• \(C^*\)-algebras by example
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