$\mathrm {SL}(2, 5)$ Has No Smooth Effective One-fixed-point Action on $S^8$

Volume 64 / 2016

Agnieszka Borowiecka Bulletin Polish Acad. Sci. Math. 64 (2016), 85-94 MSC: 57S17, 57S25. DOI: 10.4064/ba8040-3-2016 Published online: 16 May 2016

Abstract

We prove that there is no effective smooth one-fixed-point action of $\mathrm {SL}(2,5)$, the special linear group of $2\times 2$ matrices over $\mathbb {Z}_5$, on the $8$-dimensional sphere. The method of proof involves the intersection form.

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