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I have tried to give algebraic topology a better Idea-section.
One of the links (to the book :Algebraic topology from a homotopical viewpoint) is not working.
Thanks. Maybe better this way. I have replaced it with a pointer to a pdf of just the toc.
Urs, I think what you wrote is more suitable to an Overview section rather than the very idea. The idea is to study topological spaces via algebraic invariants or via functors from topological to algebraic categories. Period. Then one can also say that most (though not all, hence e.g. shape theory) useful functors are homotopy invariant.
The rest of the nice story you wrote may belong to an overview of present state of the matters, but not the very idea of the subject. If somebody does not know what algebraic topology is it will not help to hear an explanation via advanced unexplained word “spectral sequence”. I think it would be more sensitive to split the entry into sections Idea and Overview. What do you think ?
Sure, please do.
I made the splitting and extended the entry algebraic topology significantly. Please take a look.
I added few more improvements (I hope).
Okay, thanks.
(#6 has a typo in the link)
Since ’lifting’ had no link, I started lift with redirects. There will be plenty of links to put in.
Either it’s a coincidence, or maybe somebody was inspired by the above edits to ask (as you may have seen already) on MathOverflow: What is modern algebraic topology(homotopy theory) about?.
Sometimes I wish the entry hurdle to discussing on the nForum were lower. Are we sure we need to require people to apply for an account here?
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