The local index formula in semifinite von Neumann algebras. II: the even case

DOI10.1016/j.aim.2005.03.010zbMath1101.46045arXivmath/0411021OpenAlexW2010596034MaRDI QIDQ2496243

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

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/0411021

zbMATH Keywords

von Neumann algebracyclic cohomologyChern characterFredholm moduleMcKean-Singer formula

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) (K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative geometry (à la Connes) (58B34) Index theory (19K56)

Related Items (30)

The noncommutative geometry of graph \(C^*\)-algebras. I: The index theorem ⋮ SPECTRAL FLOW, INDEX AND THE SIGNATURE OPERATOR ⋮ 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 ⋮ Kadison's Pythagorean theorem and essential codimension ⋮ Non-commutative Chern numbers for generic aperiodic discrete systems ⋮ Pseudo-Riemannian spectral triples and the harmonic oscillator ⋮ Equivariant \(KK\)-theory for non-Hausdorff groupoids ⋮ Index theory and topological phases of aperiodic lattices ⋮ A twisted spectral triple for quantum \(SU(2)\) ⋮ Callias-type operators associated to spectral triples ⋮ Thermal time as an unsharp observable ⋮ The noncommutative geometry of k-graph C*-algebras ⋮ The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podleś sphere ⋮ Integral Formula for Spectral Flow for -Summable Operators ⋮ The spectral localizer for semifinite spectral triples ⋮ The spectral shift function and spectral flow ⋮ The \(K\)-theoretic bulk-edge correspondence for topological insulators ⋮ The Dixmier trace and asymptotics of zeta functions ⋮ 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 ⋮ Two-cocycle twists and Atiyah–Patodi–Singer index theory ⋮ The Godbillon-Vey invariant and equivariant \(KK\)-theory ⋮ Local index formulae on noncommutative orbifolds and equivariant zeta functions for the affine metaplectic group ⋮ KK-Theory and Spectral Flow in von Neumann Algebras

Cites Work

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• Algebras almost commuting with Clifford algebras in a \(II_{\infty}\) factor
• The Chern character of semifinite spectral triples
• An index theorem for Toeplitz operators with noncommutative symbol space
• 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
• The local index formula in noncommutative geometry
• The local index formula in semifinite von Neumann algebras. I: Spectral flow
• Fredholm theories in von Neumann algebras. I
• Fredholm theories in von Neumann algebras. II
• Unbounded Fredholm Modules and Spectral Flow

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