info prev up next book cdrom email home

Vector Bundle

A special class of Fiber Bundle in which the Fiber is a Vector Space. Technically, a little more is required; namely, if $f: E\to B$ is a Bundle with Fiber $\Bbb{R}^n$, to be a vector bundle, all of the Fibers $f^{-1}(x)$ for $x \in B$ need to have a coherent Vector Space structure. One way to say this is that the ``trivializations'' $h: f^{-1}(U)\to U\times\Bbb{R}^n$, are Fiber-for-Fiber Vector Space Isomorphisms.

See also Bundle, Fiber, Fiber Bundle, Lie Algebroid, Stable Equivalence, Tangent Map, Vector Space, Whitney Sum

© 1996-9 Eric W. Weisstein