A noncommutative Atiyah-Patodi-Singer index theorem in KK-theory

Details A noncommutative Atiyah-Patodi-Singer index theorem in KK-theory A noncommutative Atiyah-Patodi-Singer index theorem in KK-theory

2007-11-19

arxiv.org/abs/0711.3028v2

Mathematics

K-Theory and Homology

40 pages, minor corrections to final section

Scientific paper

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.

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