New aspects of the ddc-lemma
By G. Cavalcanti. 2005
109 citations recorded by the source corpus.
We produce examples of generalized complex structures on manifolds by generalizing results from symplectic and complex geometry. We produce generalized complex structures on symplectic fibrations over a generalized complex base. We study in some detail different invariant generalized complex structures on compact Lie groups and provide a thorough description of invariant structures on nilmanifolds, achieving a classification on 6-nilmanifolds. We study implications of the `dd^c-lemma' in the generalized complex setting. Similarly to the standard dd^c-lemma, its generalized version induces a decomposition of the cohomology of a manifold and causes the degeneracy of the spectral sequence associated to the splitting d = \del + \delbar at E_1. But, in contrast with the dd^c-lemma, its generalized version is not preserved by symplectic blow-up or blow-down (in the case of a generalized complex structure induced by a symplectic structure) and does not imply formality.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/959284699ee13a9ec9fc0f7c2b615c15de73d789
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Algebraic models in geometry (2008, background): “This question is answered negatively by Cavalcanti [52] and we will take it up in Chapter 8.”
- Hamiltonian Symmetries and Reduction in Generalized Geometry (2005, methodology): “The early version of this work appeared on the arXiv along with the works of Lin-Tolman [36], Bursztyn-Cavalcanti-Gualtieri [14] as well as Stienon-Xu [54] around the same time.”