One of my favorite theorems is the Seifert-van Kampen theorem. It’s a very handy result in algebraic topology which allows us to calculate the fundamental group of complicated spaces by breaking them down into simpler spaces. The version of the theorem I’ll be using here can be stated as follows: Let be a path connectedContinue reading “Using the Seifert-van Kampen theorem to calculate the fundamental group of the torus, aided by illustrations from mspaint”