Abstract
In this paper, we first extend Smith, Thomas and Yau’s examples of certain symplectic conifold transitions on trivial \({\mathbb {C}}P^{1}\)-bundles over K ähler surfaces to all \({\mathbb {C}}P^{1}\)-bundles over symplectic 4-manifolds. Then we determine the diffeomorphism types of all these symplectic conifold transitions. In particular, this implies that in the case of trivial \({\mathbb {C}}P^{1}\)-bundles over projective complex surfaces, Smith, Thomas and Yau’s examples of symplectic conifold transitions are diffeomorphic to Kähler three-folds.
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Jiang, Y. Topology of certain symplectic conifold transitions of \(\mathbb {C} P^{1}\)-bundles. Math. Z. 281, 1171–1182 (2015). https://doi.org/10.1007/s00209-015-1525-5
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DOI: https://doi.org/10.1007/s00209-015-1525-5
Keywords
- Symplectic conifold transitions
- \({\mathbb {C}}P^{1}\)-bundles
- Kähler three-folds
- Characteristic classes