Dolbeault cohomology for almost complex manifolds

2018/09/05 by Cirici, Joana, Wilson, Scott O.
#Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.01416

Abstract

This 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 Kähler 6-manifolds, and show Dolbeault cohomology can be used to prohibit the existence of nearly Kähler metrics.

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