Flat bundles, von Neumann algebras andK-theory with ℝ/ℤ-coefficients

DOI10.1017/is014001024jkt253zbMath1315.46077arXiv1308.0218OpenAlexW2963314197MaRDI QIDQ3191176

Sara Azzali, Georges Skandalis, Paolo Antonini

Publication date: 24 September 2014

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

Full work available at URL: https://arxiv.org/abs/1308.0218

zbMATH Keywords

flat bundles\(\mathbb{R}/\mathbb{Z}\)-\(K\)-theory\(\Pi_1\)-factorsrelative eta invariant

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Eta-invariants, Chern-Simons invariants (58J28) Index theory (19K56)

Related Items (12)

Index theory on the Miščenko bundle ⋮ Realizing the analytic surgery group of Higson and Roe geometrically. II: Relative \(\eta\)-invariants ⋮ The Atiyah-Patodi-Singer mod k index theorem for Dirac operators over \(C^*\)-algebras ⋮ Topological \(K\)-theory with coefficients and the \(e\)-invariant ⋮ Bivariant \(K\)-theory with \(\mathbb{R}/\mathbb{Z}\)-coefficients and rho classes of unitary representations ⋮ The Baum–Connes conjecture localised at the unit element of a discrete group ⋮ The Novikov conjecture, the group of volume preserving diffeomorphisms and Hilbert-Hadamard spaces ⋮ The adiabatic groupoid and the Higson-Roe exact sequence ⋮ Noncommutative differential \(K\)-theory ⋮ Eta and rho invariants on manifolds with edges ⋮ Chern-Simons invariants in \textit{KK}-theory ⋮ Analytic Pontryagin duality

Cites Work

• The \(KK\)-product of unbounded modules
• Théorie générale des classes caractéristiques secondaires. (General theory of secondary characteristic classes)
• The analysis of elliptic families. II: Dirac operators, êta invariants, and the holonomy theorem
• The residue of the global eta function at the origin
• The odd Chern character in cyclic homology and spectral flow
• Characteristic classes of holomorphic or algebraic foliated fiber bundles.
• The relation between the Baum-Connes conjecture and the trace conjecture
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• Spectral flow in Fredholm modules, eta invariants and the JLO cocycle
• \(\mathbb{R} /\mathbb{Z}\) index theory
• The Godbillon-Vey cyclic cocycle and longitudinal Dirac operators
• Cyclic cocycles, renormalization and eta-invariants
• Spectral asymmetry and Riemannian Geometry. I
• Spectral asymmetry and Riemannian geometry. II
• Spectral asymmetry and Riemannian geometry. III
• Type II Spectral Flow and the Eta Invariant

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