= Quaternionic projective space
{title2=$\mathbb{HP}^n$}
{wiki}
Quaternionic projective space is the space of right quaternionic lines in $\mathbb H^{n+1}$. It is $S^{4n+3}$ modulo the right action of unit <quaternions>, with one cell in each dimension $0,4,\ldots,4n$. It is a compact smooth manifold of real dimension $4n$; $\mathbb{HP}^1\cong S^4$. The <quaternionic tautological line bundle> and its <sphere bundle> give the multiplication in its <cohomology ring of quaternionic projective space>.
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