Cohomology of D-complex manifolds

Daniele Angella; Federico A. Rossi

doi:10.1016/j.difgeo.2012.07.003

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arXiv · 1201.2503

Cohomology of D-complex manifolds

Daniele Angella·Federico A. Rossi

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Abstract

In order to look for a well-behaved counterpart to Dolbeault cohomology in D-complex geometry, we study the de Rham cohomology of an almost D-complex manifold and its subgroups made up of the classes admitting invariant, respectively anti-invariant, representatives with respect to the almost D-complex structure, miming the theory introduced by T.-J. Li and W. Zhang in [T.-J. Li, W. Zhang, Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom. 17 (2009), no. 4, 651-684] for almost complex manifolds. In particular, we prove that, on a 4-dimensional D-complex nilmanifold, such subgroups provide a decomposition at the level of the real second de Rham cohomology group. Moreover, we study deformations of D-complex structures, showing in particular that admitting D-Kaehler structures is not a stable property under small deformations.

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BibTeX RIS

Daniele Angella, Federico A. Rossi. 2012-01-12. Cohomology of D-complex manifolds. https://doi.org/10.1016/j.difgeo.2012.07.003

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