 

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


Published: 
August 7, 2009

Keywords: 
Index theory, cyclic homology, KKtheory, spectral flow 
Subject: 
19D55,58G12,19K35 


Abstract
We prove index formulas for elliptic operators acting between spaces of sections of C*vector bundles on a closed manifold. The formulas involve Karoubi's Chern character from Ktheory of a C*algebra to de Rham homology of smooth subalgebras. We show how they apply to the higher index theory 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 Ktheory and KKtheory to the noncommutative spectral flow and prove the regularity of elliptic pseudodifferential operators over C*algebras.


Acknowledgements
This research was funded by a grant of AdvanceVT


Author information
LeibnizForschungsstelle der Göttinger Akademie der Wissenschaften, Waterloostr. 8, 30169 Hannover, Germany
wahlcharlotte@googlemail.com

