  The fragmentation of an unpolarized quark into a transversely polarized
spin-1/2 particle is studied in the framework of a simple model. Special
attention is payed to the gluon exchange which is incorporated in the gauge
link of the fragmentation function, and which we model by an abelian gauge
field. The transverse single spin asymmetries in $e^+ e^-$ annihilation and
semi-inclusive deep-inelastic scattering are calculated in the one-loop
approximation. For $e^+ e^-$ annihilation one finds a cancellation between
contributions from two on-shell intermediate states, which have no counterpart
in deep-inelastic scattering. As a consequence of this cancellation, the model
predicts the same spin asymmetry for both processes implying that, in the
one-loop approximation, the corresponding fragmentation function is universal.
