Abstract
The goal of this lecture will be to use linear algebra and group theroy in order to understand topological spaces up to continuous deformations.
Organisation
The course will take place every Thursday 8.30am-11.45am from September 11st to December 11th, 2025.
The exercise session will take place every Monday 8.30am-11.45am from September 15th to December 8th, 2025.
Until October 6th (included), Bruno Vallette will teach the exercise session and, after October 13th (included), it will be João Lourenco.
Main reference
We will mainly follow the excellent, concise and complete book "
Topologie Algébrique" by Yves Félix and Daniel Tanré published by Dunod (256 pages).
Lecture Notes
The recollection notes on the definition of topological spaces and the product topology is available here:
Schedule
- September 15th: Exercices 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7 (pages 24-25).
- September 11th: Homotopy (Section 1.1).
Exams, homeworks and worksheets (2024)
- Exam 1:
- Exam 2:
- Exam 3:
- Homework 2:
- Worksheet (December 3rd):
Beyond the lectures
- Analysis situs: great website dedicated to the works of Poincaré on the algebraic topology of manifolds.
- Voyages aux pays des maths: episode of this great series (watch the other ones!) dedicated to the Poincaré conjecture.
Other references
- Algebraic Topology: A First Course, Marvin J. Greenberg and John R. Harper, Mathematics Lecture Note Series, 58, The Benjaming/Cummings Publishing Company.
- Algebraic Topology, Allen Hatcher, Cambridge University Press, 2001.
- A concise course in Algebraic Topology, J. Peter May, Chicago Lectures in Mathematics, 1999.
Follow-up
- Homotopy theories (Master 2 Mathematics,Fundamental Courses II, November-December 2024).
Seminars
Teachers
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Last updates: September 11, 2025.