Questions tagged [tangent-bundle]

I want to prove that the tangent bundle of open annulus is diffeomorphic to $\mathbb{S}^1 \times \mathbb{R}^3$. This arguments came from mathoverflow I have no clue of constructing this, any rudimental information will be helpful. I have some basic…

From Lee's introduction to smooth manifolds: Proposition $3.18$. The tangent bundle of a smooth $n$-manifold has a natural smooth structure that makes it into a $2n$-dimensional smooth manifold. Since I wanted to know how the atlas is defined, I…

If we have a set $X=A\cup B$ and $Y= A\cap B$. What is the difference between $TY$ (the tangent bundle of $Y$) and $T_{Y}X$ (the tangent bundle of $X$ at $Y$)? That is, $Y$ is subset of $X$, so I can not understand what we mean by tangent bundle of…

This is a extension of my former question [Tangent bundle of open annulus is diffeomorphic to $\mathbb{S}^1 \times \mathbb{R}^3$ Now i want to show the tangent bundle $\mathbb{S}^1 \times \mathbb{R}^3$. I tried to construct the similar method, but…