University of Illinois at Urbana-Champaign

Math 490 Section M2 (Topology of Surfaces) Spring 2006

Course Description

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 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.


In-class handouts:


Note: extra class session on Wed, 4/26 from 5 - 5:30 pm.