Bundles Definition and 56 Threads

Hey, I'm a little confused on the definition of a principle bundle. The basic question: "Do elements of the structure group, G, have to act on elements of the fiber, G, from the right?" I've read a bunch of papers that seem to imply that the fiber bundle structure group elements could act...

I need help solving the following problem: Let M,N be differentiable manifolds, and f\in C^\infty(M,N). We say that the fields X\in \mathfrak{X}(M) and Y \in \mathfrak{X}(N) are f-related if and only if f_{*p}(X(p))=Y_{f(p)} for all p\in M. Prove that: (a) X and Y are f-related if and only if...

I try to understand the notion of connections on fibre bundles from the lecture notes http://arxiv.org/abs/math-ph/9902027" by George Svetlichny. On page 27 stands what the attached picture shows. (I don't know whether the attached picture will be visible, so I copy the text here: )...

Hello, I've 2 qustions : 1.Calculus the tangent bundel TM and the cotangent bundles T*M like a bundles associates to the principal bundle B(M) of the reper of TM 2.If M has a riemannian structure set up the principale bundels B'(M) of orthonormal system of TM in case of M=S^2 , we can...

Good morning, Can you help me to find a corses on vector and principale bundles and spinorielle geometry :rolleyes: thanks

i was wondering what happens where an infinite number of lightbeams meet in one point/knot in open space or anywhere.. how come they do'nt mess up one another? is this on account of their being massless? ..anything we see, any lightbeam that reaches our eye is crossed infinite times by beams...