COURSE DESCRIPTION
An introduction to the fundamental group: homotopy and path homotopy, homotopy
equivalence, basic calculations of fundamental groups, fundamental group of the
circle and applications (for instance to retractions and fixed-point theorems),
van Kampen's theorem, covering spaces, universal covers. Examples of all of the
above. Instructor may choose further topics such as deck transformations and the
Galois correspondence, basic homology, compact surfaces.
Prerequisites: Math 190A
Model answers to the first midtermModel answers to the second midterm
RECENT UPDATE
[06.06.2025] The final will be mostly focused on homotopy theory the material relating to Lectures 15 t0 19 and Homework 5 to 8.