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A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
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Vector bundles on Grassmannians
Let $Gr(k,n)$ be the Grassmannian of $k$-dimensional vector subspaces $H^k$ of an $n$-dimensional vector space $V$.
Let us fix an $h$-dimensional vector subspace $\Gamma\subset V$ with $h\leq k$, and …