  Sometimes a homology cycle of a nonsingular compactification manifold cannot
be represented by a nonsingular submanifold. We want to know whether such
nonrepresentable cycles can be wrapped by D-branes. A brane wrapping a
representable cycle carries a K-theory charge if and only if its Freed-Witten
anomaly vanishes. However some K-theory charges are only carried by branes that
wrap nonrepresentable cycles. We provide two examples of Freed-Witten
anomaly-free D6-branes wrapping nonrepresentable cycles in the presence of a
trivial NS 3-form flux. The first occurs in type IIA string theory compactified
on the Sp(2) group manifold and the second in IIA on a product of lens spaces.
We find that the first D6-brane carries a K-theory charge while the second does
not.
