We define a transverse Dolbeault cohomology associated to any almost complex structure on a smooth manifold . This we do by extending the notion of transverse complex structure and by introducing a natural -stable involutive limit distribution with such a transverse complex structure. We relate this transverse Dolbeault cohomology to the generalized Dolbeault cohomology of introduced by Cirici and Wilson in 2001, showing that the cohomology spaces coincide. This study of transversality leads us to suggest a notion of minimally non-integrable almost complex structure.
Cite this article
Michel Cahen, Jean Gutt, Simone Gutt, Almost complex structures, transverse complex structures, and transverse Dolbeault cohomology. Rev. Mat. Iberoam. (2023), published online firstDOI 10.4171/RMI/1450