Closed 6-manifolds built as X times S2, with X an exotic CP2#kCP2, carry cohomologous symplectic forms with different Gromov widths and different first Chern classes.
Doug Park, Exotic smooth structures on small 4-manifolds, Invent
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Cohomologous symplectic forms with different Gromov widths
Closed 6-manifolds built as X times S2, with X an exotic CP2#kCP2, carry cohomologous symplectic forms with different Gromov widths and different first Chern classes.