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

Yi Jiang

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arXiv · 1502.02447

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

Yi Jiang

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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 Kähler 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 Kähler 3--folds.

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Yi Jiang. 2015-02-09. Topology of certain symplectic conifold transitions of $CP^{1}$-bundles. https://arxiv.org/abs/1502.02447

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