The De Rham theorem and an application on the Lie group theory

Abstract

[en] The origin of the algebraic topology opened a new way to study the geometric properties through some algebraic invariants. Over the years, mathematicians have been capable of developing different bridges between these two areas. The final goal of this text is to go in depth into one of these connections: the de Rham cohomology. Likewise, we study the main result of this theory: the de Rham theorem. In this text, we obtain this result as a consequence of a more general theorem on sheaf theory. The de Rham theorem plays an essential role in the area of differential geometry where it has many implications. In the final part of this text, we explain a significant application in Lie group theory.