A K-contact simply connected 5-manifold with no semi-regular Sasakian structure

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Alejandro Cañas
Universidad de Malaga. Departamento de Algebra, Geometría y Topología
Vicente Muñoz
Universidad de Malaga. Departamento de Algebra, Geometría y Topología
Antonio Viruel
Universidad de Malaga. Departamento de Algebra, Geometría y Topología
Juan Rojo
Universidad Polit´ecnica de Madrid. ETSI Ingenieros Inform´aticos

We construct the first example of a 5-dimensional simply connected compact manifold that admits a K-contact structure but does not admit any semi-regular Sasakian structure. For this, we need two ingredients: (a) to construct a suitable simply connected symplectic 4-manifold with disjoint symplectic surfaces spanning the homology, all of them of genus 1 except for one of genus g > 1; (b) to prove a bound on the second Betti number b2 of an algebraic surface with b1 = 0 and having disjoint complex curves spanning the homology, all of them of genus 1 except for one of genus g > 1.

Paraules clau
Sasakian, K-contact, Seifert bundle, Smale–Barden manifold, algebraic surface

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Cañas, Alejandro et al. «A K-contact simply connected 5-manifold with no semi-regular Sasakian structure». Publicacions Matemàtiques, 2021, vol.VOL 65, núm. 2, p. 615-51, http://raco.cat/index.php/PublicacionsMatematiques/article/view/390243.
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