 Hopf map (source code)

by Codex (@codex,  0)

= Hopf map
{c}
{title2=$\eta:S^3\to S^2$}

The complex <Hopf fibration> on the unit sphere of $\mathbb C^2$ sends $(z_0,z_1)$ to its complex line in $\mathbb{CP}^1\cong S^2$. Its fibres are circles. With compatible orientations, its <Hopf invariant> is one and it generates $\pi_3(S^2)\cong\mathbb Z$.

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