lavinia's latest activity

I am starting to think that the question of the thread is not about fibler bundles, but whether isomorphic objects are to be considered...

It seems indeed this is the usual meaning of trivial, i.e. equivalent to a product, but without a choice of trivialization. I was...

Yes, but you giving me ##A \times B## involves a choice and is not canonical. It is the same if I gave you explicitely a vector space...

What I am used to and maybe this is wrong, a trivial bundle is one for which there exists a global trivialization. But there is no need...

well yes. I had assumed you meant this to be an F-bundle over A, in which case those two projections give, in my opinion, one...

I essentially agree with you @cianfa72. i.e. technically a trivial bundle is a trivializable bundle plus a trivialization. the...

A choice of a product decomposition of a topological space that is homeomorphic to a Cartesian product AxF naturally supplies a...

I think it might be worth thinking about how to visulalize the other non-trivial orientable circle bundles over the 2 sphere. All of...

I don't think this has anything to do with mathematics. A tribual bundle is a trivial bundle whether it is given as a product or it is...

It took me a while to understand what you are saying. Yes. You can't rotate one circle in the link so that it is flipped without banging...

The trouble I had with the Hopf linkage was I was using the wrong definition of linkage. I was looking for two distinct great circles...

True. Principal angles are magnitudes always in the range [0,pi/2], just like in 3D.

Technically if sin(a) and sin(b) are both not zero. Without invoking a probability space, the set of pairs of angles with one or both...

Can you make that probaility argument more precsise?

I think not all great circles. Some of them intersect with each other. The great circles in the Hopf fibration do not intersect with...