English

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

Symplectic Geometry 2025-03-18 v1 Differential Geometry

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.

Keywords

Cite

@article{arxiv.2503.12428,
  title  = {Constructions of symplectic surfaces in symplectic 4-manifolds with transversal intersections},
  author = {Vicente Muñoz and Juan Rojo},
  journal= {arXiv preprint arXiv:2503.12428},
  year   = {2025}
}

Comments

17 pages, no figures