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# Advances in Theoretical and Mathematical Physics

## Volume 13 (2009)

### Number 2

### Non-commutative correspondences, duality and D-branes in bivariant K-theory

Pages: 497 – 552

DOI: http://dx.doi.org/10.4310/ATMP.2009.v13.n2.a4

#### Authors

#### 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.