Bivariant algebraic K-theory

DOI10.1515/CRELLE.2007.068zbMath1152.19002arXivmath/0603531OpenAlexW2963554956WikidataQ61677706 ScholiaQ61677706MaRDI QIDQ5387207

Guillermo Cortiñas, Andreas Thom

Publication date: 8 May 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603531

zbMATH Keywords

algebraic K-theorybivariant K-theory

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55)

Related Items

Homotopy theory of associative rings ⋮ Bivariant Hermitian \(K\)-theory and Karoubi's fundamental theorem ⋮ The loop-stable homotopy category of algebras ⋮ Lifting graph C∗$C^*$‐algebra maps to Leavitt path algebra maps ⋮ Equivariant algebraic \(KK\)-theory and adjointness theorems ⋮ Graded \(K\)-theory and Leavitt path algebras ⋮ Classifying Leavitt path algebras up to involution preserving homotopy ⋮ Algebraic \(k\,k\)-theory and the KH-isomorphism conjecture ⋮ Universal bivariant algebraic \(K\)-theories ⋮ Isomorphism conjectures with proper coefficients ⋮ A universal characterization of higher algebraic \(K\)-theory ⋮ Universal suspension via noncommutative motives ⋮ Algebraic v. Topological K-Theory: A Friendly Match ⋮ Homotopy invariance through small stabilizations ⋮ The homotopy groups of the simplicial mapping space between algebras ⋮ Algebraic quantum kk-theory ⋮ The Novikov conjecture for algebraic K-theory of the group algebra over the ring of Schatten class operators ⋮ Higher \(K\)-theory via universal invariants ⋮ Comparison between algebraic and topological \(K\)-theory of locally convex algebras ⋮ Cyclic homology, tight crossed products, and small stabilizations ⋮ Homotopy classification of Leavitt path algebras ⋮ Algebraic bivariant \(K\)-theory and Leavitt path algebras. ⋮ On the \(K\)-theory of pullbacks ⋮ \(\mathbb{A}^1\)-homotopy invariants of dg orbit categories

Cites Work

• The Baum-Connes conjecture via localisation of categories
• Algebraic \(K\)-theory and locally convex algebras
• Caractère de Chern bivariant. (Bivariant Chern character)
• A new look at KK-theory
• Models in solar water heating - a critical comparison
• Excision in bivariant periodic cyclic cohomology
• Delooping classifying spaces in algebraic K-theory
• Excision in bivariant periodic cyclic cohomology: A categorical approach
• Verallgemeinerung eines Satzes von Herrn F. Specker