### Abstract

We develop some of the ingredients needed for string theory on noncommutative spacetimes, proposing an axiomatic formulation of T-duality as well as establishing a very general formula for D-brane charges. This formula is closely related to a noncommutative Grothendieck-Riemann-Roch theorem that is proved here. Our approach relies on a very general form of Poincaré duality, which is studied here in detail. Among the technical tools employed are calculations with iterated products in bivariant K -theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams. © 2007 Springer-Verlag.

Original language | English |
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Pages (from-to) | 643-706 |

Number of pages | 64 |

Journal | Communications in Mathematical Physics |

Volume | 277 |

Issue number | 3 |

DOIs | |

Publication status | Published - Feb 2008 |

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## Cite this

*Communications in Mathematical Physics*,

*277*(3), 643-706. https://doi.org/10.1007/s00220-007-0396-y