Associated Fiber Bundle

Given a group action G×F->F and a principal bundle pi:A->M, the associated fiber bundle on M is


In particular, it is the quotient space A×F/G where (a,x)∼(ga,g^(-1)x).

For example, the torus T={(e^(is),e^(it))} has a S^1 action given by


and the frame bundle on the sphere,


is a principal S^1 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

Explore with Wolfram|Alpha

Cite this as:

Rowland, Todd. "Associated Fiber Bundle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

Subject classifications