The Cayley-Dickson Construction in Homotopy Type Theory

Ulrik Buchholtz, Egbert Rijke

Abstract


We define in the setting of homotopy type theory an H-space structure on $\Sn^3$. Hence we obtain a description of the quaternionic Hopf fibration $\Sn^3\hookrightarrow\Sn^7\twoheadrightarrow\Sn^4$, using only homotopy invariant tools.

 


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