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arXiv · 2503.12428

Constructions of symplectic surfaces in symplectic 4-manifolds with transversal intersections

Vicente Muñoz·Juan Rojo
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Abstract

In the breakthrough paper [V. Mu\~noz, A Smale-Barden manifold admitting K-contact but not Sasakian structure, 2024, 10.4171/JEMS/1496], it is constructed the first example of a simply connected compact 5-manifold (aka.\ Smale-Barden manifold) which admits a K-contact structure but does not carry a Sasakian structure, thus settling the question raised as Open Problem 10.2.1 in n [C. Boyer and K. Galicki, Sasakian Geometry, OUP, 2007]. In this paper we revise, refine and generalize the constructions of symplectic surfaces in a symplectic 4-manifold with transversal intersections. These are needed to produce the ramification locus of Seifert bundles over symplectic 4-orbifolds that serve to produce K-contact 5-manifolds.

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Vicente Muñoz, Juan Rojo. 2025-03-16. Constructions of symplectic surfaces in symplectic 4-manifolds with transversal intersections. https://arxiv.org/abs/2503.12428

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