### Abstract

We describe a categorical framework for the classification of D-branes on non-commutative spaces using techniques from bivariant K-theory of C*-algebras. We present a new description of bivariant K-theory in terms of non-commutative correspondences which is nicely adapted to the study of T-duality in open string theory. We systematically use the diagram calculus for bivariant K-theory as detailed in our previous paper 12. We explicitly work out our theory for a number of examples of noncommutative manifolds. © 2009 International Press.

Original language | English |
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Pages (from-to) | 497-552 |

Number of pages | 56 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 13 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2009 |

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## Cite this

Brodzki, J., Mathai, V., Rosenberg, J., & Szabo, R. J. (2009). Non-commutative correspondences, duality and D-branes in bivariant K-theory.

*Advances in Theoretical and Mathematical Physics*,*13*(2), 497-552. https://doi.org/10.4310/ATMP.2009.v13.n2.a4