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edited to improve anonymity and remove unacademic language
Pete L. Clark
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"Why the heck are the homotopy groups of the sphere so damn complicated?"

This is a quote from a dear friend asking the rest of us on Facebook. I gave him some half-baked response, but the truth is I don't really know enough about this to give him a good response.

So why ARE they so complicated? The topologists here want to give a few responses so I can give him some feedback to his desperate query?