Homological index formulas for elliptic operators over C*-algebras
Charlotte Wahl

TL;DR
This paper develops index formulas for elliptic operators over C*-algebras, connecting K-theory, de Rham homology, and noncommutative geometry, with applications to coverings, foliations, and group actions.
Contribution
It introduces new index formulas involving Karoubi's Chern character for elliptic operators on C*-vector bundles, extending classical index theory to noncommutative settings.
Findings
Derived index formulas for elliptic operators over C*-algebras.
Applied formulas to higher index theorems for coverings and foliated bundles.
Established relations between K-theory pairings, spectral flow, and pseudodifferential operators.
Abstract
We prove index formulas for elliptic operators acting between sections of C*-vector bundles on a closed manifold. The formulas involve Karoubi's Chern character from K-theory of a C*-algebra to de Rham homology of smooth subalgebras. We show how they apply to the higher index theorem for coverings and to flat foliated bundles, and prove an index theorem for C*-dynamical systems associated to actions of compact Lie groups. In an Appendix we relate the pairing of odd K-theory and KK-theory to the noncommutative spectral flow and prove the regularity of elliptic pseudodifferential operators over C*-algebras.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models
