13. Barycentric subdivision
In this lecture we ruthlessly chop up simplices into smaller ones. This cruel and unusual punishment is called barycentric subdivision. The main result is that this process accomplishes nothing—the homology before and after is the same.
Whilst this may at first seem like an epic waste of time, it will turn out next lecture that our ability to grind up simplices without the homology functor noticing is exactly the tool we need to prove the excision axiom. This is the last axiom of "a homology theory", and the one that will finally allow us to start computing things.
Next Wednesday Berit is going over Problem Sheets D, E and F during the lecture. Next Friday is the 🍷 ETH Faculty Retreat 🍷, so there are is no lecture. 😀 This means that the next normal lecture will not be until Wednesday 15th November!
Comments and questions?