# Tagged Questions

Differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.

73 views

47 views

### A question about a part of the proof of the existence of the exterior derivate.

Let $M$ a differentiable manifold, $(U;x_1,\ldots,x_n)$ a coordinated system and $\omega$ a differential form which domain intersects $U$. In $U \cap \operatorname{Dom} \omega$, $\omega$ can be ...
37 views

### Schwartz rule in differentiable manifolds.

Let $M$ a differentiable manifold and $(U,\varphi)$ a chart with coordinate functions $(x_1,...,x_n)$. Let $p \in U$. Given $f:U\longrightarrow \mathbb{R}$, $f \in C^\infty(U)$, it is possible to ...
97 views

### Explicit Calculation of the Euler class for the 2-Sphere using transition functions

I have been trying to learn about characteristic classes for months now, and every time I try a simple example something goes wrong. Any insights would be greatly appreciated. I am trying to follow ...
144 views

87 views

### Two definitions of embedded submanifold

Let $N$ be a smooth manifold. One possible definition (I believe) for an embedded submanifold of $N$ is some $M \subset N$ that is a (smooth) manifold such that the inclusion $i : M \hookrightarrow N$ ...
114 views

### Reference to finite coverings causing injections on deRham cohomology

So, I've heard that if you have a finite degree covering of a compact connected manifold by another compact connected manifold of dimension $n$ (So $\pi :M \rightarrow N$) gives an injection on the ...
I am trying to get a better feel for both the exterior derivative of a form and the contraction of a form by a vector field $X$. Basically, when are these inverses? If I have a one-form $\omega$ and ...
I am trying to understand in more detail the answer to: Universal Cover of a Surface (with Boundary) It is mentioned that the universal cover of a hyperbolic surface $S$ with geodesic boundary is a ...