Wikipedia states that
In 1953 George W. Whitehead showed that there is a metastable range for the homotopy groups of spheres.
What is the metastable range? I was unable to find the definition.
2026-05-06 04:15:25.1778040925
What is metastable range?
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The metastable range refers to the existence of a long exact sequence $$\pi_{3n-2}(S^{n}) \rightarrow \cdots \rightarrow \pi_{q}(S^{n}) \rightarrow \pi_{q+1}(S^{n+1}) \rightarrow \pi_{q-1}(S^{2n-1}) \rightarrow \pi_{q-1}(S^{n}) \rightarrow \cdots$$ in the range $q \leq 3n-2$.
The relevant paper is here.