1. The Brower Fixed-Point Theorem
🎉🎉🎉 Welcome to Algebraic Topology I 🎉🎉🎉
In this first lecture we give a brief introduction to the “idea” of algebraic topology, and illustrate the concept by giving a “proof” of the Brower Fixed Point Theorem. (I say “proof” because the proof uses the homology, which we won't start for a few more lectures ...)
We then give the first few elementary definitions in Category Theory. My plan is to stealthily introduce a little bit of abstract nonsense each lecture, so that by the end of the course you will know lots without ever having been completely overwhelmed.
To “motivate” you to learn more category theory, have a read of this (by Ed Morehouse). The more category theory you know, the funnier it will be—eventually you will no doubt be unable to read it without laughing hysterically (okay, maybe that's just me ...)
My lecture notes likely have one or two (million) typos in them. Please leave a comment if you spot something wrong and I will fix it! I encourage you not to print the notes out just yet, since I'll probably edit them at least six times over the next few days (hopefully in a week or so they should be relatively stable ...)
Comments and questions?