  Friedman and Morgan made the "speculation" that deformation equivalence and
diffeomorphism should coincide for algebraic surfaces. Counterexamples, for the
hitherto open case of surfaces of general type, have been given in the last
years by Manetti, by Kharlamov-Kulikov and in my cited article. For the latter
much simpler examples, it was shown that there are surfaces $S$ which are not
deformation equivalent to their complex conjugate. However, by Seiberg-Witten
theory, any (oriented) diffeomorphism of minimal surfaces carries the canonical
class K to + K or to - K, and deformation equivalence implies the existence of
a diffeomorphism carrying K to +K. In fact, as observed by a referee, the bulk
of the proof was to show that our surfaces have no selfhomeomorphism carrying K
to - K (the same for the K-K surfaces). In this note we show that Manetti's
surfaces provide indeed a counterexample to the reinforced conjecture, since
they are symplectomorphic. Our result is that a surface of general type has a
canonical symplectic structure (up to symplectomorphism) which is invariant for
deformation and for certain degenerations to normal surfaces. Since moreover no
simply connected counterexamples to the conjecture are known, we provide
explicit families of 1-connected surfaces, which are obtained by glueing
together two fixed manifolds with boundary, are not deformation equivalent, but
are homeomorphic under a homeomorphism carrying K to +K. We also give as
application the existence of symplectically equivalent, but not deformation
equivalent cuspidal plane curves.
