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

  1. Cañas, Alejandro 2
  2. Muñoz, Vicente 2
  3. Viruel, Antonio 2
  4. Juan Ángel Rojo Carulli 1
  1. 1 Universidad Politécnica de Madrid. ETSI Ingenieros Informáticos
  2. 2 Universidad de Malaga. Departamento de Algebra, Geometría y Topología
Revista:
Publicacions matematiques

ISSN: 0214-1493

Año de publicación: 2021

Volumen: 65

Número: 2

Páginas: 615-651

Tipo: Artículo

DOI: 10.5565/PUBLMAT6522107 DIALNET GOOGLE SCHOLAR lock_openDDD editor

Otras publicaciones en: Publicacions matematiques

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.

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Información de financiación

Fran Presas, and Roger Casals for useful comments. We are also grateful to the two anonymous referees that have given us numerous comments. The second author is partially supported by Project MINECO (Spain) PGC2018-095448-B-I00. The fourth author is partially supported by Project MINECO (Spain) MTM2016-78647-P.

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