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.
