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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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vote
Accepted
Unicity of a vector field on $S^1$-bundle
Let $(M,\omega)$ be a symplectic manifold. The first idea behind geometric quantization is that there exists a $S^1$-principal fiber bundle $\pi : Y \to M$, equipped with a connection $\lambda$ with c …
2
votes
Topology of maps between fibers of vector bundles
I elaborate a little bit on what your question inspires me. I will treat a more general question, but you can reduce it to finite linear dimensional fiber bundles over manifolds. Let $\pi : E \to X$ a …