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