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This semester we went through chapter 1 of Hatcher (after spending several weeks on point set topology via Munkres) and I had to pick up the group theory I needed as we went along. It was hard, but I made it through and loved the course, so I'll be taking the next course, where I believe we'll be finishing Hatcher. My professor suggests that we'll need to know linear algebra in the form of tensors, but I was hoping to get a more complete list of topics that I can study over winter break.

(Note, there is a similar question here: Algebra prerequisites for Hatcher's Algebraic Topology but its only about the group theory requirements).

roundsquare
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    It might also help to know a bit about rings and modules. But that, too, can be picked up as you go through the book. – Jeroen van der Meer Dec 11 '21 at 13:11
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    It might also help to know about polynomial rings when you will be computing examples of cohomology rings. Chapter 2 & 3 is probably a lot more algebraic than chapter 1 since the theory of (co-)homology with require some machinery from homological algebra. But most objects will be set up in the book and many students see this material the first time when they study algebraic topology. – Qi Zhu Dec 11 '21 at 14:21
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    page 213-217 in Hatcher reviews the algebra super quickly. I think that it would be good to know the classification of finitely generated Abelian groups, the definition of an R-module and the definition of the tensor product. Given your professor's prerequisites, it seems like a lot of this will be covered in your class. Maybe this note https://www.math.brown.edu/reschwar/M153/tensor.pdf together with some examples as commented above would be enough. – Andres Mejia Dec 11 '21 at 18:44
  • Thanks all! This is very helpful. I know I can pick things up as I go along, but I'll have some time over winter break to prepare so I might as well :) – roundsquare Dec 11 '21 at 23:22

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