### D-Branes, RR-Fields and duality on noncommutative manifolds, by Jacek Brodzki, Varghese Mathai, Jonathan Rosenberg, and 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 K-theory and cyclic theory, which are
simplified using a novel
diagram calculus reminiscent of Feynman diagrams.

Jacek Brodzki <j.brodzki@soton.ac.uk>

Varghese Mathai <vmathai@maths.adelaide.edu.au>

Jonathan Rosenberg <jmr@math.umd.edu>

Richard J. Szabo <R.J.Szabo@ma.hw.ac.uk>