MATH-F419: Algebraic topology

2021

Room and Time: Wednesdays 10:00-11:00 in P.OF.2078 and Fridays 15:00-16:00 in P.1C3.203.

Course content: The idea is to associate to topological spaces algebraic objects (groups, rings etc). If this is done judiciously, one can hope for example to distinguish non-homeomorphic spaces or essentially different continuous maps (in a suitable sense). This in turn allows one to prove interesting results, for example that any continuous map from a closed ball in a finite-dimensional Euclidean space into itself has a fixed point (Brouwer’s theorem).

Lecture notes (Last updated: 09 JUN 2022)

Literature

J. Vick. Homology theory. An introduction to algebraic topology.
A. Hatcher. Algebraic Topology ( Chapters 1 and 2), available online: http://www.math.cornell.edu/~hatcher/AT/ATpage.html