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A continuously varying family of one-dimensional vector spaces over a topological space. A related tag is the vector-bundles tag.

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Is there a toplogically trivial line bundle over a compact Riemann surfaces that isn't holom... [closed]

Is a complex line bundle over a compact Riemann surface topologically trivial iff it is holomorphically trivial? If so, how does one demonstrate that, and if not, what is a counterexample?
John Robertson's user avatar