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42 votes
12 answers
7k views

Why is the definition of the higher homotopy groups the "right one"?

If someone asked me the question for the fundamental group, I would answer as follows: The connection to classification of covering spaces. The fundamental group of many spaces is an object of ...
7 votes
1 answer
2k views

Which revolutions in topology and geometry can we expect in the next 20 years? [closed]

In my limited perspective on the history of mathematics, I can name at least two big revolutions in Topology and Geometry (broadly construed): the introduction of Schemes in Algebraic Geometry, and ...
-8 votes
2 answers
861 views

Homotopy theory and algebraic topology last 10 years. Is it a dying field? [closed]

I'm under the impression that algebraic topology is a dying field in mathematics. That was my impression but I think I'm wrong. As every person I do need some evidence that my impression is not ...