A number-theoretic approach to homotopy exponents of SU(n)

Mathematics – Algebraic Topology

Scientific paper

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20 pages

Scientific paper

We use methods of combinatorial number theory to prove that, for each $n>1$
and any prime $p$, some homotopy group $\pi_i(SU(n))$ contains an element of
order $p^{n-1+ord_p([n/p]!)}$, where $ord_p(m)$ denotes the largest integer
$\alpha$ such that $p^{\alpha}$ divides $m$.

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