The local index formula in semifinite von Neumann algebras. I: Spectral flow

DOI10.1016/j.aim.2005.03.011zbMath1118.46060arXivmath/0411019OpenAlexW2063924670MaRDI QIDQ2496242

John Phillips, Adam Rennie, Pheodor A. Sukochev, Alan L. Carey

Publication date: 12 July 2006

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0411019

zbMATH Keywords

von Neumann algebraspectral flowcyclic cohomologyChern characterFredholm moduleodd local index theorem

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) (K)-theory and operator algebras (including cyclic theory) (46L80) Exotic index theories on manifolds (58J22) Noncommutative geometry (à la Connes) (58B34) Noncommutative global analysis, noncommutative residues (58J42) Index theory (19K56) Spectral flows (58J30)

Related Items (43)

The noncommutative geometry of graph \(C^*\)-algebras. I: The index theorem ⋮ Local index formula for quantum double suspension ⋮ Generalized Connes–Chern characters inKK-theory with an application to weak invariants of topological insulators ⋮ Chern numbers, localisation and the bulk-edge correspondence for continuous models of topological phases ⋮ Examples of odd index theorems ⋮ Non-commutative Chern numbers for generic aperiodic discrete systems ⋮ Pseudo-Riemannian spectral triples and the harmonic oscillator ⋮ Equivariant \(KK\)-theory for non-Hausdorff groupoids ⋮ Approximation of the spectral action functional in the case of \(\tau\)-compact resolvents ⋮ Index theory and topological phases of aperiodic lattices ⋮ A twisted spectral triple for quantum \(SU(2)\) ⋮ Callias-type operators associated to spectral triples ⋮ Index theory of chiral unitaries and split-step quantum walks ⋮ Thermal time as an unsharp observable ⋮ The JLO character for the noncommutative space of connections of Aastrup-Grimstrup-Nest ⋮ Levinson's theorem as an index pairing ⋮ Families of type III KMS states on a class of \(C^*\)-algebras containing \(O_n\) and \({\mathcal Q}_{\mathbb N}\) ⋮ The noncommutative geometry of k-graph C*-algebras ⋮ Heat trace and spectral action on the standard Podleś sphere ⋮ The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podleś sphere ⋮ Advances in Dixmier traces and applications ⋮ Integral Formula for Spectral Flow for -Summable Operators ⋮ The spectral localizer for semifinite spectral triples ⋮ The spectral shift function and spectral flow ⋮ Spectral action on noncommutative torus ⋮ The \(K\)-theoretic bulk-edge correspondence for topological insulators ⋮ Noncommutative manifolds from graph and \(k\)-graph \(C^*\)-algebras ⋮ The local index formula in semifinite von Neumann algebras. II: the even case ⋮ Twisted cyclic theory and an index theory for the gauge invariant KMS state on the Cuntz algebra O_n ⋮ The Dixmier trace and asymptotics of zeta functions ⋮ Spectral flow invariants and twisted cyclic theory for the Haar state on \(SU_q(2)\) ⋮ Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators ⋮ Untwisting twisted spectral triples ⋮ Index theory for locally compact noncommutative geometries ⋮ Twisted cyclic theory, equivariant KK-theory and KMS states ⋮ Index pairings for \(\mathbb{R}^n\)-actions and Rieffel deformations ⋮ ON THE JLO COCYCLE AND ITS TRANSGRESSION IN ENTIRE CYCLIC COHOMOLOGY ⋮ The Godbillon-Vey invariant and equivariant \(KK\)-theory ⋮ Real dimensional spaces in noncommutative geometry ⋮ Bulk-boundary correspondence for topological insulators with quantized magneto-electric effect ⋮ KK-Theory and Spectral Flow in von Neumann Algebras ⋮ Non-commutative integration, zeta functions and the Haar state for \(\mathrm{SU}_q(2)\) ⋮ Asymptotic and exact expansions of heat traces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Toeplitz operators on flows
• Algebras almost commuting with Clifford algebras in a \(II_{\infty}\) factor
• Non-commutative differential geometry
• The odd Chern character in cyclic homology and spectral flow
• An index theorem for Toeplitz operators with noncommutative symbol space
• Smoothness and locality for nonunital spectral triples
• On unbounded \(p\)-summable Fredholm modules
• Spectral flow, eta invariants, and von Neumann algebras
• Generalized s-numbers of \(\tau\)-measurable operators
• Spectral flow in Fredholm modules, eta invariants and the JLO cocycle
• Spectral flow and Dixmier traces
• The Hochschild class of the Chern character for semifinite spectral triples
• Geometry from the spectral point of view
• The local index formula in noncommutative geometry
• Fredholm theories in von Neumann algebras. I
• Fredholm theories in von Neumann algebras. II
• \(C^*\)-algebras of operators on a half-space. II: Index theory
• Unbounded Fredholm Modules and Spectral Flow
• Self-Adjoint Fredholm Operators And Spectral Flow

This page was built for publication: The local index formula in semifinite von Neumann algebras. I: Spectral flow