  We construct examples of four dimensional manifolds with Spin$^c$-structures,
whose moduli spaces of solutions to the Seiberg-Witten equations, represent a
non-trivial bordism class of positive dimension, i.e. the Spin$^c$-structures
are not induced by almost complex structures. As an application, we show the
existence of infinitely many non-homeomorphic compact oriented 4-manifolds with
free fundamental group and predetermined Euler characteristic and signature
that do not carry Einstein metrics.
