Existence and classification of b-contact structures

• Cardona, Robert ^[1] ; Oms, Cédric ^[2]
  1. [1] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
  2. [2] Basque Center for Applied Mathematics

     Basque Center for Applied Mathematics

     Bilbao, España

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 70, Nº 1, 2026, págs. 247-275
• Idioma: inglés
• DOI: 10.5565/publmat7012609
• Texto completo no disponible (Saber más ...)
• Resumen

  • A b-contact structure on a b-manifold (M, Z) is a Jacobi structure on M satisfying a transversality condition along the hypersurface Z. We show that, in three dimensions, b-contact structures with overtwisted 3-dimensional leaves satisfy an existence h-principle that allows us to prescribe the induced singular foliation. We give a method to classify b-contact structures on a given b-manifold and use it to give a classification o n S 3 with either a 2 -sphere o r an unknotted t orus as the critical surface. We also discuss generalizations to higher dimensions