The abstract should provide clear information about the research and the results obtained, and should not exceed 200 words. The abstract should not contain citations. An application of Gromov--Witten invariants is that they distinguish the deformation types of symplectic structures on a smooth manifold. In this manuscript, it is proven that the use of Gromov--Witten invariants in the class of embedded $J$-holomorphic spheres is restricted. This restriction is in the sense that they cannot distinguish the deformation types of symplectic structures on $X_1\times S^2$ and $X_2\times S^2$ for two minimal, simply connected, symplectic $4$-manifolds $X_1$ and $X_2$ with $b_2^+(X_1)>1$ and $b_2^+(X_2)>1$. The result employs the adjunction inequality for symplectic $4$-manifolds which is derived from Seiberg-Witten theory.
Symplectic manifolds, $J$-holomorphic curves, symplectic deformation equivalence
"Count of genus zero $J$-holomorphic curves in dimensions four and six,"
Turkish Journal of Mathematics: Vol. 45:
5, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss5/6