# ELEMENTS OF ADVANCED GEOMETRYModule SECOND PART

**Academic Year 2023/2024**- Teacher:

**Angelo BELLA**

## Expected Learning Outcomes

Fundamental aspects of Algebraic Topology. Principal objects of the study are the fundamental group and some relevant facts of omotopy theory.

## Course Structure

Lectures with slides. Discussion and correction of exercises.

If the teaching is given in a mixed or remote mode, the necessary changes may be introduced with respect to what was previously stated, in order to respect the program envisaged and reported in the syllabus.

## Detailed Course Content

Basic facts on algebraic topology. Homotopy theory. Degree of a function between n-spheres. Brower's theorem in general form. Singular homology groups. The exact sequence of a pair. Mayer-Vetoris's sequence. Another proof of Brower's theorem. Jordan's theory in general form.

## Textbook Information

1. Professor's notes

2. "Topologia" by M. Manetti.

3. Dugundji "Topology"