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تسجيل مستخدم جديدHolomorphic spheres and four-dimensional symplectic pairs
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We classify four-dimensional manifolds endowed with symplectic pairs admitting embedded symplectic spheres with non-negative self-intersection, following the strategy of McDuffs classification of rational and ruled symplectic four manifolds.
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We study the geometry of manifolds carrying symplectic pairs consisting of two closed 2-forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build contact-symplectic and contact pairs from symplectic pairs.
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_2(M,Z)$ with $c_1(M).beta=0$, provided that the divisibility of $beta$ is at most 4 (i.e. if $beta=nalpha$ with $alphain H_2(M,Z)$ and $nin Z$ then $nleq 4$). Moreover, each such curve is embedded and 4-rigid.
The paper was withdrawn due to a gap in the proof of Lemma 3.
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