 Associated bundle (source code)

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= Associated bundle
{title2=$P\times_G F$}

For a <principal bundle> $P\to B$ and a left action of its structure group on a manifold $F$, the associated bundle is $(P\times F)/\sim$, where $(pg,f)\sim(p,gf)$. Local sections identify it with $U\times F$; principal transition functions act on $F$. Linear actions give <associated vector bundles>.

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