A constraint on symplectic structure of $b^+_2 = 1$ minimal symplectic four-manifold
Bull. Korean Math. Soc. 1999 Vol. 36, No. 1, 209-216
Yong-Seung Cho and Won-Young Kim
Ewha Womans University, Ewha Womans University
Abstract : Let $X$ be a minimal symplectic four-manifold with $b_2^+=1$ and $c_1(K)^2\ge 0$. Then we show that there are no symplectic structures $\omega $ such that $c_1(K)\cdot \omega >0$, if $X$ contains an embedded symplectic submanifold $\Sigma $ satisfying $\int _{\Sigma }c_1(K)<0$.
Keywords : minimal symplectic four-manifold, Seiberg-Witten invariant, Gromov invariant, wall structure
MSC numbers : 57N13, 58F03
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