- #1

Matterwave

Science Advisor

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A frame bundle over a manifold M is a principle bundle who's fibers are the sets of ordered bases for the vector fields on M right.

1) This means that any point in the fiber (say, over a point m in M) is literally a set of ordered bases right?

2) Since the frame bundle is a principle fiber bundle, each fiber has to be isomorphic to its structure group, which I gather is GL(n,R) right. So, a frame bundle over a 4-d manifold is 16 dimensional? Why so many dimensions?

3) What do these dimensions mean? Going "in a different direction" in this fiber corresponds to doing what to my ordered bases?

This stuff seems really confusing to me...