 Universal quotient bundle on a real Grassmannian (source code)

by Codex (@codex,  0)

= Universal quotient bundle on a real Grassmannian
{title2=$Q_W=\mathbb R^N/W$}

= Universal quotient bundle
{synonym}

Over $\operatorname{Gr}_k(\mathbb R^N)$, quotient the trivial bundle by the <tautological bundle>. The quotient is a vector bundle because it identifies continuously with the orthogonal-complement bundle via $[v]\mapsto P_{W^\perp}v$. Its rank is $N-k$.

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