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

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

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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]

dc.contributor.authorCarey, Alan
dc.contributor.authorPhillips, John
dc.contributor.authorRennie, Adam Charles
dc.date.accessioned2015-12-10T21:57:47Z
dc.identifier.issn0075-4102
dc.identifier.urihttp://hdl.handle.net/1885/39935
dc.description.abstractWe 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.
dc.publisherWalter de Gruyter
dc.sourceJournal fur Reine und Angewandte Mathematik
dc.titleNoncommutative Atiyah-Patodi-Singer boundary conditions and index pairings in KK-theory
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume643
dc.date.issued2010
local.identifier.absfor010103 - Category Theory, K Theory, Homological Algebra
local.identifier.ariespublicationf2965xPUB186
local.type.statusPublished Version
local.contributor.affiliationCarey, Alan, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationPhillips, John, University of Victoria
local.contributor.affiliationRennie, Adam Charles, University of Copenhagen
local.description.embargo2037-12-31
local.bibliographicCitation.startpage59
local.bibliographicCitation.lastpage109
local.identifier.doi10.1515/CRELLE.2010.045
dc.date.updated2015-12-09T07:48:31Z
local.identifier.scopusID2-s2.0-77956073350
local.identifier.thomsonID000278948800004
CollectionsANU Research Publications

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