New aspects of the ddc-lemma
| dc.creator | Cavalcanti, Gil R. | |
| dc.date | 2005-01-24 | |
| dc.date.accessioned | 2026-07-07T05:16:20Z | |
| dc.date.available | 2026-07-07T05:16:20Z | |
| dc.description | 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. | |
| dc.description | Oxford University D. Phil thesis. 140 pages. This thesis contains material from the papers math.SG/0403067, math.DG/0404451, math.AT/0412053 and `T-duality and generalized complex structures', which is in preparation and is a collaboration with Gualtieri | |
| dc.identifier | https://arxiv.org/abs/math/0501406 | |
| dc.identifier | http://arxiv.org/abs/math/0501406 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73947 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 53C15; 53C80; 32Q55; 53D35 | |
| dc.title | New aspects of the ddc-lemma | |
| dc.type | text |