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Noncommutative atiyah-patodi-singer boundary conditions and index pairings in KK-theory

Journal Article


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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-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

Publication Date


  • 2010

Citation


  • Carey, A. L., Phillips, J. & Rennie, A. C. (2010). Noncommutative atiyah-patodi-singer boundary conditions and index pairings in KK-theory. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal, 2010 (643), 59-109.

Scopus Eid


  • 2-s2.0-77956073350

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1696&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/690

Number Of Pages


  • 50

Start Page


  • 59

End Page


  • 109

Volume


  • 2010

Issue


  • 643

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-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

Publication Date


  • 2010

Citation


  • Carey, A. L., Phillips, J. & Rennie, A. C. (2010). Noncommutative atiyah-patodi-singer boundary conditions and index pairings in KK-theory. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal, 2010 (643), 59-109.

Scopus Eid


  • 2-s2.0-77956073350

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1696&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/690

Number Of Pages


  • 50

Start Page


  • 59

End Page


  • 109

Volume


  • 2010

Issue


  • 643