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Post Reopened by teil, Yemon Choi, Emerton, Qiaochu Yuan, Tyler Lawson
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Yemon Choi
Yemon Choi
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Greg Muller, in a post called Rational Homotopy TheoryRational Homotopy Theory on the blog "The Everything Seminar" wrote

"I tend to think of homotopy theory a little bit like ‘The One That Got Away’ from mathematics as a whole. Its full of wistful fantasies about how awesome it would have been if things could only have worked out. Imagine if homotopy groups of spaces and homotopy classes of maps were as easy to compute as homology groups…"

What are the wonderful consequences that he is referring to?

Greg Muller, in a post called Rational Homotopy Theory on the blog "The Everything Seminar" wrote

"I tend to think of homotopy theory a little bit like ‘The One That Got Away’ from mathematics as a whole. Its full of wistful fantasies about how awesome it would have been if things could only have worked out. Imagine if homotopy groups of spaces and homotopy classes of maps were as easy to compute as homology groups…"

What are the wonderful consequences that he is referring to?

Greg Muller, in a post called Rational Homotopy Theory on the blog "The Everything Seminar" wrote

"I tend to think of homotopy theory a little bit like ‘The One That Got Away’ from mathematics as a whole. Its full of wistful fantasies about how awesome it would have been if things could only have worked out. Imagine if homotopy groups of spaces and homotopy classes of maps were as easy to compute as homology groups…"

What are the wonderful consequences that he is referring to?

Post Closed as "not a real question" by Mariano Suárez-Álvarez, S. Carnahan♦, Ryan Budney, François G. Dorais, Harry Gindi
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teil
teil
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What would be the ramifications of homotopy theory being as easy as homology theory?

Greg Muller, in a post called Rational Homotopy Theory on the blog "The Everything Seminar" wrote

"I tend to think of homotopy theory a little bit like ‘The One That Got Away’ from mathematics as a whole. Its full of wistful fantasies about how awesome it would have been if things could only have worked out. Imagine if homotopy groups of spaces and homotopy classes of maps were as easy to compute as homology groups…"

What are the wonderful consequences that he is referring to?