Welcome to the cosmos of Low Dimensional Topology. This is the area of mathematics that deals with the study of smooth manifolds of dimensions less than 5. We will explore the land of exotic shapes and geometries that arise from these low dimensional curiosities. Somehow, the dimensional constraints offered by these objects (such as knots, surfaces, 3 and 4-manifolds) manifest some of the most interesting geometric phenomena.

While certainly beautiful, the downside to this subject is that it requires a lot of machinery to even define (and work with) these objects. The purpose of this course is to provide an overview of some essential ideas in point-set topology, differential topology, and algebraic topology and expose students to the aromas and flavors of low dimensional topology before they might usually encounter them. That being said, this class is NOT meant to be a replacement for more structured classes in geometry and topology (e.g. Math 140, 141, 142, 202a, 214, 215a/b, etc.), but we hope to be a helpful supplement to motivate and introduce a lot of the concepts taught more in depth in said classes and, moreover, touch on some applications that are typically withheld until further study.

Lectures will be held on Monday, Wednesday, and Friday, and will be centered around introducing new material. Lecture Attendance is worth 30% of your grade! If you don't attend the lecture section or you are more than 10 minutes late (10 minutes after "Berkeley time") then you will be marked as absent. You will be allowed two unexcused lecture absences for the Fall term that won't be factored into your overall Attendance Grade. In the case of emergency, an absence will only be excused if you provide documentation. The overall grade breakdown will be 30% attendence, 70% homework. Homework will be assigned on a weekly basis and graded for accuracy, but the final grade of your homework will be mostly by completion.