Homological index formulas for elliptic operators over C*-algebras

2006/03/30 by Charlotte Wahl, Wahl, Charlotte
Mathematics · #19D55 #19K35 #58G12 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.math/0603694

openalex publication_date 2006/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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