MHB What Are the Best Resources for Learning Homology Theory?

AI Thread Summary
Homology theory is a complex subject that requires a solid understanding of algebraic topology. Members of the forum suggest approaching the topic through formal texts rather than those that are overly conceptual or "hand-wavy." A recommended resource is the book by Vick, which provides a formal introduction, particularly in its first chapter. Another useful text is "Introduction to Topological Manifolds" by Lee, noted for its careful motivation and clarity in arguments. Conversely, Hatcher's book is strongly discouraged due to its lack of rigor. Overall, the emphasis is on finding resources that balance motivation with formalism to aid in understanding the fundamentals of homology theory.
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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
 
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Peter said:
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.
 
ThePerfectHacker said:
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
 
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