Exploring Frame Bundles on Manifolds

In summary: M is a principle GL(n,R)-bundle who's fibers are the sets of ordered bases for the tangent space of M at p. (where n=dim(M))"1) This means that any point in the fiber (say, over a point m in M) is literally a set of ordered bases right?Yes, it is literally an n-tuple of vectors spanning TmM.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
  • #36
For the sake of background: I ended up studying bundles by mistake:

My girlfriend wanted to take a class in cosmetology, but she misread the

instructions in the webpage, and ended up registering for cosmology instead

. Since there were no refunds, and she knew no math,I had to help her.

Then I became interested in bundles.
 
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  • #37
haha, funny story. :)

But how do bundles pop-up in cosmology?!?
 
  • #38
Even in graduate GR, I never had to use bundles for cosmology, seems weird. XD
 
  • #39
Not really no bundles that I know of in cosmology ; just a contrivance to do a bad joke.
 
  • #40
Ah I see. We sure fell for it. :P
 

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