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Associated Fiber Bundle

المؤلف:  المرجع الالكتروني للمعلوماتيه

المصدر:  www.almerja.com

الجزء والصفحة:  ...

22-5-2021

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Associated Fiber Bundle

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 {(e^(is),e^(it))}" src="https://mathworld.wolfram.com/images/equations/AssociatedFiberBundle/Inline6.gif" style="height:21px; width:82px" /> 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.