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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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What are some applications of virtual vector bundles?

K-theory gives a nice way to define vector bundles that don't actually exist. For example, given a singular variety $Y$ embedded into a smooth variety $X$ we can define the virtual normal bundle as $$ …