2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72384In this lecture, we review some of the concepts of generalized geometry, as introduced by Hitchin and developed in the speaker's thesis. We also prove a Hodge decomposition for the twisted cohomology of a compact generalized Kähler manifold, as well as a generalization of the $dd^c$-lemma of Kähler geometry.Lecture at the String Theory and Geometry workshop, August 2004, Oberwolfach. 7 pagesDifferential Geometry53C15; 53C55; 53C80text