**Cours fondamental 1 ** (TA)

** Contact :** `ausoni à univ-paris13.fr`

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

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.

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

- Tammo tom Dieck. Algebraic Topology.
*EMS Textbooks in Mathematics, 2008*https://www.ems-ph.org/books/book.php?proj_nr=86 - Peter May. A concise course in Algebraic Topology.
*Chicago Lectures in Mathematics, 1999*https://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf - Allen Hatcher. Algebraic Topology.
*Cambridge University Press, 2001*http://pi.math.cornell.edu/~hatcher/AT/ATpage.html - Edward B. Curtis. Simplicial homotopy theory.
*Advances in Mathematics 6, 107-209, 197*https://www.sciencedirect.com/science/article/pii/0001870871900156