Synopsis. This 4-credit course is one of the core offerings in our graduate mathematics program. It provides an introduction to associating algebraic invariants to topological spaces. The main topics are: the fundamental group, covering spaces, van Kampen's theorem, the Eilenberg–Steenrod Axioms for homology, axioms for cohomology, homology groups of spheres and applications, CW-complexes and cellular homology, real and complex projective spaces, singular homology, the Künneth Formula, cohomology and cup and cap products, manifolds and orientations, Poincaré and Lefschetz duality. Further topics are covered in Algebraic Topology II, MATH 7530.
Textbooks. Allen Hatcher, Algebraic Topology (downloadable for free from Hatcher's web site) and Steven Weintraub, Fundamentals of Algebraic Topology (downloadable from our library). Hatcher provides a guide to other texts.
Prerequisites. Minimally, some point-set topology and abstract algebra, mainly group theory. Ideally, our MATH 4530 or similar.
Two take-home midterms. Provisionally, 27 February–6 March & 10–17 April.
Presentations. Details are here.
Assessment. Homework 50%, midterms 15% each, presentation 15%, class and office hours participation 5%. No final exam is planned.
Add / drop dates etc.