A noncommutative Atiyah-Patodi-Singer index theorem in KK-theory
K-Theory and Homology
2008-02-04 v2 Operator Algebras
Abstract
We investigate an extension of ideas of Atiyah-Patodi-Singer (APS) to a noncommutative geometry setting framed in terms of Kasparov modules. We use a mapping cone construction to relate odd index pairings to even index pairings with APS boundary conditions in the setting of KK-theory, generalising the commutative theory. We find that Cuntz-Kreiger systems provide a natural class of examples for our construction and the index pairings coming from APS boundary conditions yield complete K-theoretic information about certain graph C*-algebras.
Keywords
Cite
@article{arxiv.0711.3028,
title = {A noncommutative Atiyah-Patodi-Singer index theorem in KK-theory},
author = {A. L. Carey and J. Phillips and A. Rennie},
journal= {arXiv preprint arXiv:0711.3028},
year = {2008}
}
Comments
40 pages, minor corrections to final section