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Licensed Unlicensed Requires Authentication Published by De Gruyter June 21, 2010

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

  • A. L. Carey , J. Phillips and A. Rennie

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.

Received: 2007-11-19
Revised: 2009-02-03
Published Online: 2010-06-21
Published in Print: 2010-June

© Walter de Gruyter Berlin · New York 2010

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