Bounding size of homotopy groups of spheres

Guy Boyde

Let $p$ be prime. We prove that, for $n$ odd, the $p$-torsion part of ${\pi }_q(S^n)$ has cardinality at most $p^{2^{\frac{1}{p-1}(q-n+3-2p)}}$, and hence has rank at most $2^{\frac{1…