Credits: 9

Type: advanced

Knowledge:

The relation of several geometric properties with the topological properties of differentiable manifolds; the De Rham theorem and Poincaré duality; an introduction to the concepts of differential topology and symplectic geometry.

Course topics:

• Singular cohomology.
• Differential forms and De Rham cohomology.
• Orientation of manifolds.
• Duality theorems for manifolds.
• Elements of differential topology.
• Symplectic manifolds.

Subject-specific competences:

• To be able to calculate and compare singular cohomology with de Rham cohomolgy of compact differentiable manifolds.
• To show understanding of Poincaré duality and some of its consequences.
• To build and use Morse functions.
• To use specific tools in symplectic geometry.