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arXiv 2015-02-09 0 views

Topology of certain symplectic conifold transitions of CP¹-bundles

Jiang, Yi

Original · EN

In this paper, we prove the existence of certain symplectic conifold transitions on all CP¹-bundles over symplectic 4--manifolds, which generalizes Smith, Thomas and Yau's examples of symplectic conifold transitions on trivial CP¹-bundles over Kähler surfaces. Our main result is to determine the diffeomorphism types of such symplectic conifold transitions of CP¹-bundles. In particular, this implies that in the case of trivial CP¹-bundles over projective surfaces, Smith, Thomas and Yau's examples of symplectic conifold transitions are diffeomorphic to Kähler 3--folds.

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