Cohomologies on hypercomplex manifolds

Abstract

We review some cohomological aspects of complex and hypercomplex manifolds and underline the differences between both realms. Furthermore, we try to highlight the similarities between compact complex surfaces on one hand and compact hypercomplex manifolds of real dimension 8 with holonomy of the Obata connection in SL(2,H) on the other hand.

Contribution to the proceedings of the "INdAM Meeting Complex and Symplectic Geometry" held in Cortona 2016