In Differential topology 46 years later (page 807, bottom of left column) Milnor states that for $n \neq 4, 125, 126$ if the order of the stable homotopy groups $|\Pi_n|$ is known then we can compute the number of exotic spheres $|S_n|$. I understand that in dimension 4 we cannot apply the $h$-cobordism theorem and $|S_4|$ is therefore unknown. I also understand that dimension 126 is as of now unresolved. What is not clear to me is what happens in $n=125$. Could someone help me and explain to me what happens in dimension 125?
2026-03-25 20:34:43.1774470883
What happens in dimension 125?
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