Given a group action and a principal
bundle ,
the associated fiber bundle on is

(1)

In particular, it is the quotient space where .

For example, the torus has a action given by

(2)

and the frame bundle on the sphere,

(3)

is a principal
bundle. The associated fiber bundle is a fiber bundle on the sphere, with fiber the
torus. It is an example of a four-dimensional manifold .

See also Bundle ,

Fiber Bundle ,

Group Action ,

Principal
Bundle ,

Quotient Space
This entry contributed by Todd
Rowland

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Cite this as:
Rowland, Todd . "Associated Fiber Bundle." From MathWorld --A Wolfram Web Resource, created by Eric
W. Weisstein . https://mathworld.wolfram.com/AssociatedFiberBundle.html

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