Turkish Journal of Mathematics
Abstract
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.
DOI
10.3906/mat-2007-72
Keywords
Symplectic manifolds, $J$-holomorphic curves, symplectic deformation equivalence
First Page
1949
Last Page
1958
Recommended Citation
BEYAZ, AHMET
(2021)
"Count of genus zero $J$-holomorphic curves in dimensions four and six,"
Turkish Journal of Mathematics: Vol. 45:
No.
5, Article 6.
https://doi.org/10.3906/mat-2007-72
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss5/6
