Homological index formulas for elliptic operators over C*-algebras

Details Homological index formulas for elliptic operators over C*-algebras Homological index formulas for elliptic operators over C*-algebras

2006-03-30

arxiv.org/abs/math/0603694v2

Mathematics

K-Theory and Homology

30 pages; discussion of flat foliated bundles included, changes mainly in introduction, section 4.1 and references

Scientific paper

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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