KK-Theory and Spectral Flow in von Neumann Algebras

DOI10.1017/is012003003jkt185zbMath1260.19001arXivmath/0701326OpenAlexW2199417231MaRDI QIDQ3143530

Adam Rennie, Jens Kaad, Ryszard Nest

Publication date: 30 November 2012

Published in: Journal of K-Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701326

zbMATH Keywords

von Neumann algebraspectral flowKK-theoryspectral triple

Mathematics Subject Classification ID

Noncommutative topology (46L85) Noncommutative differential geometry (46L87) (K)-theory and operator algebras (including cyclic theory) (46L80) Kasparov theory ((KK)-theory) (19K35) Index theory (19K56)

Related Items (12)

Chern numbers, localisation and the bulk-edge correspondence for continuous models of topological phases ⋮ Constructing KMS states from infinite-dimensional spectral triples ⋮ Callias-type operators associated to spectral triples ⋮ The Cayley transform in complex, real and graded K-theory ⋮ The spectral localizer for semifinite spectral triples ⋮ The \(K\)-theoretic bulk-edge correspondence for topological insulators ⋮ Spectral triples for noncommutative solenoidal spaces from self-coverings ⋮ Spectral flow invariants and twisted cyclic theory for the Haar state on \(SU_q(2)\) ⋮ Index theory for locally compact noncommutative geometries ⋮ Index pairings for \(\mathbb{R}^n\)-actions and Rieffel deformations ⋮ The Godbillon-Vey invariant and equivariant \(KK\)-theory ⋮ Hecke operators in \(KK\)-theory and the \(K\)-homology of Bianchi groups

Cites Work

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• Fredholm theories in von Neumann algebras. II
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• Unbounded Fredholm Modules and Spectral Flow
• Self-Adjoint Fredholm Operators And Spectral Flow
• Unbounded Fredholm Operators and Spectral Flow

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