Almost complex structures, transverse complex structures, and transverse Dolbeault cohomology

• Michel Cahen ^[1] ; Jean Gutt ^[2] ; Simone Gutt ^[1]
  1. [1] Université Libre de Bruxelles

     Université Libre de Bruxelles

     Arrondissement Brussel-Hoofdstad, Bélgica

     
  2. [2] Université Toulouse III-Paul Sabatier; Institut National Universitaire Champollion, Albi, France
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 4, 2024, págs. 1505-1527
• Idioma: inglés
• DOI: 10.4171/RMI/1450
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• Resumen

  • We define a transverse Dolbeault cohomology associated to any almost complex structure j on a smooth manifold M. This we do by extending the notion of transverse complex structure and by introducing a natural j-stable involutive limit distribution with such a transverse complex structure. We relate this transverse Dolbeault cohomology to the generalized Dolbeault cohomology of (M,j) introduced by Cirici and Wilson in 2001, showing that the (p,0) cohomology spaces coincide. This study of transversality leads us to suggest a notion of minimally non-integrable almost complex structure.