Seminar in Real and Complex Geometry

Thursday, December 16, 2021, 16:00-17:30, online (via zoom)

Roberto Rubio
(Universitat de Barcelona)

Generalized complex geometry and three-manifolds


Generalized geometry is a unifying approach to geometric structures where, for example, complex and symplectic structures become particular instances of a more general structure: a generalized complex structure. After a self-contained introduction to generalized complex geometry (which is only possible for even-dimensional manifolds), I will explain how generalized geometry can be upgraded to Bn-generalized geometry, in which the generalized-complex approach applies as well to odd dimensions. Finally, I will comment on some ongoing joint work with J. Porti in which we look at the case of three-manifolds.