Abstract
We construct a new homotopy fibration at the prime 5, involving $E_{8}$ and Harper’s rank two finite mod-5 $H$-space. We then use this to show that the 5-primary homotopy exponent of $E_{8}$ is bounded above by $5^{31}$, which is at most one power of 5 from being optimal.
Citation
Stephen D. Theriault. "The 5-primary homotopy exponent of the exceptional Lie group $E_8$." J. Math. Kyoto Univ. 44 (3) 569 - 593, 2004. https://doi.org/10.1215/kjm/1250283084
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