  In string theory D-branes can be classified by the RR-charge they carry. In
the simplest case the quantized RR-charge takes values in K-theory of the
spacetime manifold. However, if the D-brane worldvolume is not spin^c or if
there is a background B-field present, the Freed-Witten anomaly cancellation
condition requires the RR-charge to take values in twisted K-theory. Twisted
K-theory can be defined using the language of noncommutative geometry, thus
opening up a possibility for noncommutative generalizations, in particular of
the Minasian-Moore formula for the classical approximation of the charge (as
was done in arXiv:hep-th/0607020v3). A friendly introduction to these topics is
given.
