I've been looking for a definition of "trivialisation of normal bundle".
I think I understand what a vector bundle, fibre bundle and a local trivialisation of either is. I also know what a tangent bundle is.
I'm not too sure about what a normal bundle is. Let's consider the torus $T = S^1 \times S^1$. This should be a particularly easy example since it's orientable and hence if considered as the total space over the base space $X = S^1$, the fibre bundle is a trivial bundle. What does the normal bundle of $T$ look like? I think I see what the tangent bundle looks like. I assume to keep it simple we want to take the inclusion map $T \hookrightarrow \mathbb R^3$ as our immersion. Is the normal bundle $\{0\}$ at each point? If yes, can someone give me an immersion so that the normal bundle becomes more interesting? Thanks loads.
I quote from ncatlab: A framing is a trivialisation of the normal bundle of a manifold. What is a trivialisation of the normal bundle? It's also not clear to me whether "local trivialisation" and "trivialisation" are used interchangeably.