The subject of this topics course is geometric/combinatorial topology. As such it complements the two other advanced undergraduate courses in topology and geometry (Math 423: Differential Geometry of Curves and Surfaces, and Math 432: Set Theory and Topology). The highlight of the course and our principal aim is the classification theorem for compact connected surfaces, which we will prove by an explicit combinatorial argument. Along the way we will encounter applications of ideas and techniques from geometric topology in a variety of other contexts: differential equations and vector fields, algebra, knot theory, graph theory and map colorings, to name a few.
Contents
Lecture Log and homework assignments
You are encouraged to work on the homework in groups, although each student should submit a separate set of solutions. (Please indicate which other students you collaborated with, if any.) Class participation and discussion will be an important component of your grade.
Homework | 20% |
Project | 10% |
Midterm | 30% |
Final | 40% |