Cirici, JoanaWilson, Scott O.2021-12-232021-11-190001-8708https://hdl.handle.net/2445/181976This paper extends Dolbeault cohomology and its surrounding theory to arbitrary almost complex manifolds. We define a spectral sequence converging to ordinary cohomology, whose first page is the Dolbeault cohomology, and develop a harmonic theory which injects into Dolbeault cohomology. Lie-theoretic analogues of the theory are developed which yield important calculational tools for Lie groups and nilmanifolds. Finally, we study applications to maximally non-integrable manifolds, including nearly Kählerapplication/pdfengcc-by (c) Cirici, Joana et al., 2021http://creativecommons.org/licenses/by/3.0/es/Varietats complexesGeometria diferencial globalHomologiaComplex manifoldsGlobal differential geometryHomologyinfo:eu-repo/semantics/article7148512021-12-23info:eu-repo/semantics/openAccess