MATE-4425 Geometry of Differential Forms

The objective of this course is to introduce the use of modern and classic tools and machinery of a differential nature used in geometry of varieties. The course contents are: Differential varieties. Vector fields on differential varieties. Differential forms and operations with differential forms. Integration of differential forms and Stokes’ theorem. De Rham’s Theorem and Poincare’s lemma. Riemannian structures, Laplacian operator and Hodge’s theorem. Vector fibrations, connections and characteristic classes.




Cardona Guio Alexander