The teaching assistant for this course is Joost Nuiten.
Week 39: The lecture will take place on Wednesday 23rd, 10:30-12:30, room HG00.108
Course description >
This course offers an introduction to algebraic topology, that is, the study of topological spaces by means of algebra. The first part of the course focuses on homology theory. Singular homology groups are algebraic invariants of spaces: for every space there are such groups and every map of spaces induces a map between the corresponding groups. These invariants turn out to be rather computable, and they allow for some immediate geometric applications. We will establish some key properties of these homology groups like the homotopy invariance and the excision theorem.
A convenient variant is provided by singular homology with coefficients --a framework which makes necessary a short discussion of basic homological algebra including tensor and torsion products. For CW-complexes, there is also the more combinatorial cellular homology theory. The course culminates in a proof that singular homology and cellular homology agree on CW-complexes. This allows for more explicit calculations in examples of interest (e.g., projective spaces).
Lecture notes >
Exercise sheets >
Wednesday 20th January, room HG03.054 (Huygensgebouw)
Friday 22nd January, room HG03.722 (Huygensgebouw)