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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.

5 votes
1 answer
979 views

Is a complex vector bundle over a punctured closed surface trivial?

Let $M$ be a connected closed surface (possibly with non-zero genus) and let $P\subset M$ be a nonempty finite set of points. Set $\dot{M} = M \setminus P$. Let $\pi : E \rightarrow \dot{M}$ be a comp …
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