Credits: 7.5

Type: bridging

Objectives:

• To define the singular homography of topological spaces.
• To use homography to deduce various classical theorems and a number of the properties of topological manifolds.
• To study examples of group actions over space in order to introduce the theory of covering spaces.

Knowledge:

• Singular homography.
• Brouwer's fixed point theorem.
• Theorems of dimension invariance and domain invariance.
• Separation theorems.
• Covering spaces and fundamental groups.

Subject-specific competences:

• To be able to calculate the singular homography of simplicial complexes and finite cell complexes.
• To understand and apply the calculation of local homography to topological manifolds.
• To understand and use the correspondence that exists between the classes of isomorphism in covering spaces and the classes of subgroup conjugation in fundamental groups.