Cours fondamental 1 (TA)

# Homotopy 1

### Christian Ausoni (Travaux dirigés par Gabriel Angelini-Knoll)

Contact : ausoni à univ-paris13.fr

Notes de cours : https://www.math.univ-paris13.fr/~ausoni/m2-2022.html

## Présentation

This lecture course serves as an introduction to the homotopy theory of topological spaces and simplicial sets.
We will introduce homotopy groups, compute them in some examples, and study their properties and the relationship to singular homology theory.
We will then define generalized (co)-homology theories and conclude with the example of stable homotopy.
This lecture course also provides prerequisites and motivating examples for the sequel lecture course "Homotopie 2" by Geoffroy Horel.

## Contenu

• Homotopy theory of topological spaces
• Basic simplicial homotopy theory
• (Stable) homotopy groups
• Generalized (co-)homology theories

## Prérequis

Basic point-set topology, as well as basic notions of category theory, homological algebra and singular homology (as covered in the cours introductif "Théorie de l'homologie" by Baptise Rognerud).