Summary

Homology is one of the most important tools to study topological spaces and it plays an important role in many fields of mathematics. The aim of this course is to introduce this notion, understand its properties and learn how to compute it. There will be many examples and applications.

Content

Keywords

Homology, cohomology, cell complexes

Learning Prerequisites

Required courses

- Metric and topological spaces

- Topology

Recommended courses

- Group Theory

- Rings and Modules

Learning Outcomes

By the end of the course, the student must be able to:

• Define the main concepts introduced in the course
• state the theorems covered in the course and give the main ideas of their proofs
• apply the results covered in the course to examples
• compute the homology groups of CW complexes
• prove easy topological facts
• express topological arguments

Teaching methods

lectures, exercise classes, a major part of the course will be taught in the flipped classroom format.

Expected student activities

Attending the course, doing the weekly assignments, participating acclassestively in the course and the exercise

Assessment methods

Assignments, written exam

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés

Supervision

Resources

Bibliography

Algebraic Topology », Allen Hatcher

Algebraic Topology », Tammo Tom Dieck

Ressources en bibliothèque

• (version électronique)
• Algebraic Topology / Dieck
• Algebraic Topology / Hatcher

Moodle Link

• https://go.epfl.ch/MATH-323