The Hodge Decomposition Theorem - An Alternative Approach

Abstract

The famous Hodge decomposition theorem relates the topology of compact Kähler manifolds to the complex structure it is endowed with. More precisely, it states that the de Rham cohomology groups can be decomposed into the Dolbeault cohomology groups of corresponding degree. The usual proof of this theorem is highly computational. In this thesis we give an alternative proof using certain objects which arise naturally in the context of generalized complex geometry, without explicitly using the general theory.