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-Krieger 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. © Walter de Gruyter Berlin . New York 2010.
CITATION STYLE
Carey, A. L., Phillips, J., & Rennie, A. (2010). Noncommutative Atiyah-Patodi-Singer boundary conditions and index pairings in KK-theory. Journal Fur Die Reine Und Angewandte Mathematik, (643), 59–109. https://doi.org/10.1515/CRELLE.2010.045
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