Introduction to Homotopy Theory

Grégory Ginot

Abstract:

The aim of the course is to give an introduction to some tools of modern homotopy theory and its applications. We will follow primarily two examples: topological spaces and chain complexes (as seen in an algebraic topology or homological algebra class). We will focus on the modern axiomatic of homotopy incarnated by the model categories of Quillen and explain the relationship in between topological spaces and simplicial sets. If time permits it, we will give an introduction to rational homotopy to show how the mutliplicative structures of (de Rham or singular) cochains encodes homotopy type of spaces.