Connections (principal bundles) ....

[kent davidge]

I read about connections on principal bundles. I don't have the knowledge nor the time to learn about principal bundles in the first place. Never the less this makes me wonder if such connections are the same as those talked about in the context of tangent vector spaces. Are they the same thing?

 

[fresh_42]

I read about connections on principal bundles. I don't have the knowledge nor the time to learn about principal bundles in the first place. Never the less this makes me wonder if such connections are the same as those talked about in the context of tangent vector spaces. Are they the same thing?

Yes, equipped with an additional, continuous group operation which allows to jump from one point to another via elements of the group.

 

[lavinia]

Connections on principal bundles are more general and in general do not correspond to an affine connection on the tangent bundle. One can formulate the usual idea of an affine connection in terms of a connection on the principal bundle of linearly independent tangent frames.

 

[martinbn]

If you don't have the time for principal bundles in general, you could read up on bundles of frames.