Reading materials and handouts

  • You had to make and cut the Möbius strip on your first assignment. Here is a cool video of various cutting experiments you can do with the Möbius strip.

  • Yes, open and closed sets are frustrating...

  • Wikipedia page on homeomorphisms. Clicking on the picture of the coffee mug will lead you to a video of a homeomorphism between the coffee mug and a donut.

  • Here is a discussion, mostly philosophical and among mathematicians, about why we use open sets to define a topology and base the entire subject on them.

  • A video demonstrating the stereographic projection, and a video elaborating on some of its cool features.

  • Here is a handout on separation axioms, Urysohn Lemma, and Tietze Extension Theorem. We will cover some parts of this material in class.

  • A video on the Jordan Curve Theorem. Here is the Wikipedia page, and here is another page explaining it. Here is a discussion on why this result isn’t “obvious”.

  • A video on Smale’s inversion of the sphere. Here is a shorter version.

  • Here is a page that talks about various properties of the n-sphere. In particular, it explains why the 3-sphere is the union of two solid tori glued along their boundary. The Wikipedia page on the 3-sphere is also pretty good.

    • Knot theory is a large subfield of (low-dimensional) topology. Here is a song about the hardest knot of them all...

    • Here is a good page on the fundamental group. And here is a video of the proof that the fundamental group of the torus is abelian.

    • Here is a article about triangulations of manifolds, and here is an article about the solution of an open problem in triangulations that was recently solved. Here is another one, written by the person who solved the problem.

    • Here is the page about the Monster group. We know how to construct a space that has any finite group as its fundamental group, so there is a space out there that has the Monster as its fundamental group!

  • Here are some links for applications of topology: