Minicourse on Generalized Complex Geometry
Henrique Bursztyn , IMPA, Verao 2006
- Syllabus:
- Review of symplectic/complex/Kahler geometry,
definition of generalized complex structures.
- Geometry of TM+ T*M, the Courant
bracket;
Symmetries of the Courant bracket, $B$-fields;
- Exact Courant algebroids, twist by a 3-form (gerbes).
- Dirac structures, Lie algebroids and bialgebroids.
- Different points
of view to generalized complex structures; Dirac geometry and pure spinors.
- Generalized Darboux Theorem;
- Generalized complex submanifolds, branes.
- Generalized Kahler geometry, relation with bihermitian geometry;
- Introduction to the deformation theory of generalized complex structures;
- Other topics: Stable forms, T-duality, symmetries and reduction...
- References :
- Gualtieri, M.: Generalized complex geometry, PhD thesis, Oxford (2004). Arxive
math.DG/0401221.
- Hitchin, N.: Generalized Calabi-Yau manifolds. Arxive math.DG/0209099.
.
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