This course covers some essential elements of algebraic topology. This will be covered, very broadly, in three parts:
Part 1: Homology
Part 2: Cohomology
Part 3: Selected topics drawing on duality, infinite cyclic covers, characteristic classes
Please note that Math 426 (or similar) is an essential prerequisite. In particular, familiarity with the fundamental group will be assumed.
The image on the right was borrowed from The Inverse Homotopy by Tom Hockenhull (with permission); read the entire comic strip here.