| Course: | MTH 3107, Topology II |
| Instructor: | Alex Suciu |
| Time and Place: | Mon. & Wed. at 5:30 - 7:00 PM, in 109 RY |
| Office Hours: | TBA |
| Prerequisites: | MTH 3105, Topology I |
| Textbook: | Topology and Geometry, by Glen Bredon, Springer-Verlag, GTM #139 |
This course is an introduction to homology theory. We will start with singular homology theory: axioms, homological algebra, homology with coefficients, Mayer-Vietoris sequence, degrees of maps, Euler characteristic. Next, we will introduce CW-complexes and study cellular homology. We will illustrate these techniques by many geometrical examples (surfaces, projective spaces, grassmanians, lens spaces, products, etc), and derive various applications (Jordan Curve Theorem, Borsuk-Ulam Theorem, Brouwer and Lefschetz-Hopf Fixed Point Theorems, etc). Time permitting, we will touch upon cohomology theory and duality on compact manifolds.
The grade for the course will be based on problem sets, a term project, and a take-home final exam.
Created: December 29, 1995. Last modified: December 29, 1995