Intrinsic Chern-Connes Characters for Crossed Products by Zᵈ

الأصل · EN

We present a natural imbedding of the crossed product A ξZᵈ into the C-algebra of adjointable operators over the standard Hilbert A-module Hₐ. By replacing the representations on Hilbert spaces with this canonical imbedding, we define Fredholm modules and corresponding Chern-Connes characters that are intrinsic to the C-dynamical system (A,ξ,Zᵈ). The compression of the Dirac operator against projectors from A ξZᵈ produces generalized Fredholm operators over Hₐ and Mingo's index defines a KK-map from K₀(A ξZᵈ) to K(A). Using a generalized Fedosov principle and a generalized Fedosov formula, we prove an index formula for the pairing of the intrinsic Chern-Connes characters and K₀(A ξZᵈ). This pairing takes values in the image of K₀(A) in R under a canonical trace. A local index formula enables new applications in condensed matter physics to the so called weak topological invariants.