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Noncommutative Atiyah-Patodi-Singer boundary conditions and index pairings in KK-theory

Carey, Alan; Phillips, John; Rennie, Adam Charles

Description

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...[Show more]

CollectionsANU Research Publications
Date published: 2010
Type: Journal article
URI: http://hdl.handle.net/1885/39935
Source: Journal fur Reine und Angewandte Mathematik
DOI: 10.1515/CRELLE.2010.045

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