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Topology of certain symplectic conifold transitions of $CP^{1}$-bundles

Published 9 Feb 2015 in math.GT and math.SG | (1502.02447v1)

Abstract: In this paper, we prove the existence of certain symplectic conifold transitions on all $CP{1}$-bundles over symplectic 4--manifolds, which generalizes Smith, Thomas and Yau's examples of symplectic conifold transitions on trivial $CP{1}$-bundles over K\"ahler surfaces. Our main result is to determine the diffeomorphism types of such symplectic conifold transitions of $CP{1}$-bundles. In particular, this implies that in the case of trivial $CP{1}$-bundles over projective surfaces, Smith, Thomas and Yau's examples of symplectic conifold transitions are diffeomorphic to K\"ahler 3--folds.

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