Math 60330: Basic Geometry and Topology, Fall 2017

Lecture Diary

08/23: Introduced quotient topology (can read about this in Munkres's book "Topology"). Discussed some basic examples, including taking quotients of spaces by group actions. Introduced real projective space, spheres, 2-torus, Mobius band, Klein bottle. Showed some basic relationships between them. For the basics of surfaces, I recommend taking a look at either Massey's book "Algebraic Topology: An Introduction" or Armstrong's book "Basic Topology" (both of which do way more than I will do).

08/25: Talked about surfaces some more. Also talked about graphs and the weak topology. All of this can be found in Munkres and Massey.

08/28: I introduced CW complexes. A nice source for what I covered (and more) is Chapter 0 of Hatcher's book (he alternates between calling them cell complexes and CW complexes; I will try to stick with calling them CW complexes). My lectures basically covered pages 5-8.

08/30: I introduced covering spaces, basically covering Chapter 2 of my (forever unfinished) book here.

09/01: I talked about lifts and covering space morphisms, basically covering Chapter 3 of my book.