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arxiv: 1502.02447 · v1 · pith:DTN4UYU4new · submitted 2015-02-09 · 🧮 math.GT · math.SG

Topology of certain symplectic conifold transitions of CP¹-bundles

classification 🧮 math.GT math.SG
keywords symplecticbundlesconifoldtransitionsahlercertainexamplessmith
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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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