Given a group action and a principal
the associated fiber bundle on is
In particular, it is the quotient space where .
For example, the torus has a action given by
and the frame bundle on the sphere,
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.
, Fiber Bundle
, Group Action
, Quotient Space
This entry contributed by Todd
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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