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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.
6
votes
Accepted
Chern classes of a mapping torus vector bundle in terms of the construction data
In the case that $E$ is trivial, there is a "universal" example of the construction you describe, which is the vector bundle on $S^1\times U(n)$ formed the "canonical" automorphism (each point acts o …
7
votes
Accepted
Different definitions of "charged spinors": "bundle splicing" vs. "twisted spinor bundles"
I'll assume that the vector space "$V$" occuring in constructions (1) and (2) doesn't have to be the same. In that case I'll rename vector space in construction (2) to "$W$."
Then I claim that constru …