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

• Cañas, Alejandro ^[2] ; Muñoz, Vicente ^[2] ; Viruel, Antonio ^[2] ; Juan Ángel Rojo Carulli ^[1]
  1. [1] Universidad Politécnica de Madrid

     Universidad Politécnica de Madrid

     Madrid, España

     
  2. [2] Universidad de Málaga

     Universidad de Málaga

     Málaga, España

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 65, Nº 2, 2021, págs. 615-651
• Idioma: inglés
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• Resumen

  • 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.