Geodesic
SEIBERG-WITTEN INVARIANTS AND (ANTI-)SYMPLECTIC INVOLUTIONS
Glasgow mathematical journal, Tome 45 (2003) no. 3, pp. 401-413

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DOI

Let $X$ be a closed, symplectic 4-manifold. Suppose that there is either a symplectic or an anti-symplectic involution $\sigma : X\,{\to}\, X$ with a 2-dimensional compact, oriented submanifold $\Sigma$ as a fixed point set.If $\sigma$ is a symplectic involution then the quotient $X/\sigma$ with $b_2^+(X/\sigma)\,{\ge}\, 1$ is a symplectic 4-manifold.If $\sigma$ is an anti-symplectic involution and $\Sigma$ has genus greater than 1 representing non-trivial homology class, we prove a vanishing theorem on Seiberg-Witten invariants of the quotient $X/\sigma$ with $b_2^+(X/\sigma)\,{ >}\,1.$If $\Sigma$ is a torus with self-intersection number 0, we get a relation between the Seiberg-Witten invariants on $X$ and those of $X/\sigma$ with $b_2^+(X), b_2^+(X/\sigma)\,{ >}\,2$ which was obtained in [21] when the genus $g(\Sigma)\,{ >}\,1$ and $\Sigma\cdot\Sigma\,{=}\,0$.This work was supported by a Korea Research Foundation Grant (No KRF-2002-072-C00010).
DOI : 10.1017/S0017089503001344
Mots-clés : 53D05, 57M12, 57M50, 57R17, 57R57, 57S25 
CHO, YONG SEUNG; HONG, YOON HI. SEIBERG-WITTEN INVARIANTS AND (ANTI-)SYMPLECTIC INVOLUTIONS. Glasgow mathematical journal, Tome 45 (2003) no. 3, pp. 401-413. doi: 10.1017/S0017089503001344
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     title = {SEIBERG-WITTEN {INVARIANTS} {AND} {(ANTI-)SYMPLECTIC} {INVOLUTIONS}},
     journal = {Glasgow mathematical journal},
     pages = {401--413},
     year = {2003},
     volume = {45},
     number = {3},
     doi = {10.1017/S0017089503001344},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001344/}
}
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