An associated bundle is a fiber bundle constructed from a principal bundle 
with structure group 
and a left group
action of 
on a space 
.
It is the quotient 
,
where 
.
Its fiber is 
.
When 
is a vector space and the action is linear, the result
is an associated vector bundle.
Associated Bundle
See also
Fiber Bundle, Principal Bundle, Vector BundleExplore with Wolfram|Alpha
References
Husemoller, D. Fibre Bundles, 3rd ed. New York: Springer-Verlag, 1994.Cite this as:
Weisstein, Eric W. "Associated Bundle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AssociatedBundle.html