On the Chern character of a theta-summable Fredholm module

DOI10.1016/0022-1236(89)90102-XzbMath0686.46044MaRDI QIDQ1262511

András Szenes, Ezra Getzler

Publication date: 1989

Published in: Journal of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

Chern characterboundary operatortheta-summable Fredholm module over a Banach algebra with unit

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80)

Related Items (47)

Equivariant bivariant cyclic theory and equivariant Chern-Connes character ⋮ Noncommutative geometry and conformal geometry. II: Connes-Chern character and the local equivariant index theorem ⋮ The noncommutative infinitesimal equivariant index formula. II. ⋮ Superconnections and higher index theory ⋮ Index map, \(\sigma\)-connections, and Connes-Chern character in the setting of twisted spectral triples ⋮ Supersymmetry and Fredholm modules over quantized spaces ⋮ Lebesgue measure in infinite dimension as an infinite-dimensional distribution ⋮ Superspace formulation of the Chern character of a theta-summable Fredholm module ⋮ The noncommutative family Atiyah-Patodi-Singer index theorem ⋮ Algebraic index theorem ⋮ The equivariant noncommutative Atiyah-Patodi-Singer index theorem ⋮ Equivariant cyclic homology and equivariant differential forms ⋮ Constructing KMS states from infinite-dimensional spectral triples ⋮ The JLO character for the noncommutative space of connections of Aastrup-Grimstrup-Nest ⋮ Perturbations and operator trace functions ⋮ Noncommutative geometry and theoretical physics ⋮ A Hilbert bundle description of differential \(K\)-theory ⋮ Geometry on the quantum Heisenberg manifold ⋮ Loop groups and noncommutative geometry ⋮ Deformations of super-KMS functionals ⋮ The asymptotic Connes–Moscovici characteristic map and the index cocycles ⋮ Quantum K-theory. II: Homotopy invariance of the Chern character ⋮ Noncommutative geometry and conformal geometry: I. Local index formula and conformal invariants ⋮ Index theory and noncommutative geometry: a survey ⋮ Index theory for quasi-crystals. I: Computation of the gap-label group ⋮ Connes–Chern character for manifolds with boundary and eta cochains ⋮ The Chern-Connes character for the Dirac operator on manifolds with boundary ⋮ Thom elements and bivariant cyclic cohomology ⋮ Spectral flow as winding number and integral formulas ⋮ The equivariant Dirac cyclic cocycle ⋮ \(N=2\) superconformal nets ⋮ Spectral triples and the super-Virasoro algebra ⋮ Bivariant Chern character and longitudinal index ⋮ Algebra cochains and cyclic cohomology ⋮ Multiplicativity of the JLO-character ⋮ Index pairing with Alexander-Spanier cocycles ⋮ On the Lefschetz problem in noncommutative geometry. ⋮ Equivariant entire cyclic cohomology. I: Finite groups ⋮ The Chern character of \(\vartheta \)-summable Fredholm modules over dg algebras and localization on loop space ⋮ Odd characteristic classes in entire cyclic homology and equivariant loop space homology ⋮ Quantum harmonic analysis and geometric invariants ⋮ ON THE JLO COCYCLE AND ITS TRANSGRESSION IN ENTIRE CYCLIC COHOMOLOGY ⋮ Hecke operators in \(KK\)-theory and the \(K\)-homology of Bianchi groups ⋮ Transgression and the Chern character of finite-dimensional K-cycles ⋮ Cyclic cocycles in the spectral action ⋮ The equivariant family index theorem in odd dimensions ⋮ The Noncommutative Infinitesimal Equivariant Index Formula

Cites Work

• Non-commutative differential geometry
• Some algebraic properties of cyclic homology groups
• Quantum K-theory. I: The Chern character
• Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules
• The odd Chern character in cyclic homology and spectral flow
• Unnamed Item

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