Friday, July 26, 2013 - from 16:30 to 16:55
We introduce the generalized complex structures combining complex and symplectic geometry. Then we construct the category of Lie algebroids in contrast that of Lie groupoids. We understand the generalized complex structures in this bigger category and interpret the geometrical behaviour with the cocept of Lie algebroids. We describe K theory, Chow ring, de Rham cohomology, Chern characters and intersection theory. We also mention the appearance of infinite category.