Cours introductif (TA)

Théorie de l'homologie / Homology theory

christian ausoni

Contact : ausoni à math.univ-paris13.fr

Notes de cours : https://www.math.univ-paris13.fr/~ausoni/m2-2019.html

Présentation

This lecture course will provide an introduction to category theory, homological algebra and homotopy theory, with a view point motivating the modern developments of the theory by means of higher categories.

Contenu

Introduction to category theory
Homotopy groups
Simplicial sets
Basic homological algebra
Homology theories

Prérequis

Basic topology (for example Chapters 1 to 4 of the book Topology by James R. Munkres) and basic commutative algebra

Bibliographie

Tammo tom Dieck. Algebraic Topology. EMS Textbooks in Mathematics (2008) https://www.ems-ph.org/books/book.php?proj_nr=86&titleindex=1
Allan Hatcher. Algebraic Topology. Cambridge University Press (2002) http://pi.math.cornell.edu/~hatcher/AT/ATpage.html
Glen Bredon. Geometry and Topology. Springer (1993) https://www.springer.com/us/book/9780387979267