What Are the Best Resources for Learning Homology Theory?

[Math Amateur]

I would like to gain an understanding of the basics of Homology theory.

Can MHB members please give some guidance as to how to approach this endeavour.

What do MHB members suggest are good texts or good online resources?

Peter

 

[ThePerfectHacker]

I would like to gain an understanding of the basics of Homology theory.

Can MHB members please give some guidance as to how to approach this endeavour.

What do MHB members suggest are good texts or good online resources?

Peter

The problem I had with learning algebraic topology is that so many books are hand-wavy. I understand they do that because they want to try to motivate but it seems most of these authors forget that the people learning the subject need to see it done formally too and cannot just wave their hands as simply as the authors do.

A pretty formal book on homology is by Vick. I used it for chapter one and I was pretty satisfied with it. You can read chapter one from that book. But it is sometimes a little concise.

You can also read the last chapter from "Introduction to Topological Manifolds". Lee motivates and carefully does his arguments.

Never use Hatcher. That book is awful.

 

[Math Amateur]

The problem I had with learning algebraic topology is that so many books are hand-wavy. I understand they do that because they want to try to motivate but it seems most of these authors forget that the people learning the subject need to see it done formally too and cannot just wave their hands as simply as the authors do.

A pretty formal book on homology is by Vick. I used it for chapter one and I was pretty satisfied with it. You can read chapter one from that book. But it is sometimes a little concise.

You can also read the last chapter from "Introduction to Topological Manifolds". Lee motivates and carefully does his arguments.

Never use Hatcher. That book is awful.

Thanks so much for your advice ... Most helpful

Peter