Communications in Mathematical Physics

, Volume 277, Issue 3, pp 643–706 | Cite as

D-Branes, RR-Fields and Duality on Noncommutative Manifolds

  • Jacek Brodzki
  • Varghese MathaiEmail author
  • Jonathan Rosenberg
  • Richard J. Szabo


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 \(\mathsf K\)-theory and cyclic theory, which are simplified using a novel diagram calculus reminiscent of Feynman diagrams.


Chern Character Cyclic Homology Fundamental Class Spectral Triple Cyclic Cohomology 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Jacek Brodzki
    • 1
  • Varghese Mathai
    • 2
    Email author
  • Jonathan Rosenberg
    • 3
  • Richard J. Szabo
    • 4
  1. 1.School of MathematicsUniversity of SouthamptonSouthamptonUK
  2. 2.Department of Pure MathematicsUniversity of AdelaideAdelaideAustralia
  3. 3.Department of MathematicsUniversity of MarylandCollege ParkUSA
  4. 4.Department of Mathematics and Maxwell Institute for Mathematical SciencesHeriot-Watt UniversityRiccarton, EdinburghUK

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