Noncommutative correspondences, duality and D-branes in bivariant K-theory

Abstract

We describe a categorical framework for the classification of D-branes on noncommutative spaces using techniques from bivariant K-theory of C*-algebras. We present a new description of bivariant K-theory in terms of noncommutative 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. We explicitly work out our theory for a number of examples of noncommutative manifolds.

36 pages

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Cited by in corpus (4)

• Nonassociative geometry and twist deformations in non-geometric string theory
• Quantization via Linear homotopy types
• D-Branes in Orientifolds and Orbifolds and Kasparov KK-Theory
• Algebraic K-theory, K-regularity, and T-duality of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras