Bundles: first definitions

[@nikoulei5041]

Thank you for making the videos! They helped me a lot!

[@stilingiceland1403]

Thanks for the course. I really like the clear math concept definition.

[@MKWKezer]

Great video! In the last part, I was confused at first, thinking "TG is trivial" to mean TG = 0 as vector spaces - but that was only silly me. This result is beautiful, though. I guess it says, in some sense, that Lie groups come with certain symmetries and "look the same locally".

[@jmafoko]

A teacher per excellence

[@tamirbuqaie557]

Great amazing

[@jmafoko]

A pedogogical motivation for fibre bundles is product space. A trivial bundle is simply F x B. A fibre bundle is a sum of 'local' product spaces u x F s.t u in B. Vector bundle is bundle whose fibre is a vector. More precisely a bundle is a subjective map E to B , where E is sum of local products of F x u ( local trivial fibration). The map is important to define sections. Sections are a generalization of functions which is why bundle theory was invented in the first place. As langrange said 'mathematics is a study of function'. All mathematical theories are just a fancy way of talking about functions.

[@loganreina2290]

In the Lie Group example, I am confused by the notation dg(v). I assume that he is abusing notation and calling the map that multiplies by g (either on the left or the right take your pick) by the same group element that the map is derived from, g. There is still one more issue though. Where is the differential dg being evaluated? I assume since we are showing how the tangent spaces at all other points are induced by the structure of the tangent space at the identity that this is supposed to mean that dg is being evaluated at the identity. With these notational remarks I can see how this would obviously be the image of v under the differential of g at the identity. Have I interpreted this correctly?

[@fawzyhegab]

I get "no connection" error everytime I play this video eventhoug all other videos work well.