Stabilization of 4-manifolds

The complex surface X obtained by 8 points blown up on CP2 and Barlow’s surface Y are homeomorphic,but not diffeomorphic.Using the Gromov-Witten invariant Ruan showed that the stabilized manifolds X×S2and Y×S2are not deformation equivalent.In this note,we show that the stabilized manifolds X×S1and Y×S1are diffeomorphic and non-deformation equivalent in cosymplectic sense.

GENUS MINIMIZING IN SYMPLECTIC 4-MANIFOLDS

The authors show that a symplectically embedded surface in a symplectic 4-manifold with hi greater than one minimizes genus in its homology class.