$\text{SO}(4)$ and $S^3$. ($\text{SO}(4)$ och $S^3$.) (Swedish. English summary)

Normat 55, No. 3, 136-137, 144 (2007).

Summary: The 3-dimensional sphere can be thought of as a union of two solid tori glued along their boundaries. Those come from torus-fibrations, and this short note explores some elementary facts of how $\text{SO}(4)$ operates on them with connections to Hopf fibrations and quaternionic multiplication.