MATH-F419: Algebraic topology

2022

Room and Time: As a rule, Thursdays 10:00-12:00 in P.FORUM.I.2078.
However, 22.09 14:00-16:00 in P.A2.222, 07.11 10:00-12:00 in P.FORUM.I.2078

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: 01 DEC 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