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Results tagged with differential-topology
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user 1708
The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
2
votes
a small questions about hopf theorem
Suppose you have two maps $f$ and $g$ with common regular point p, and that each map has Brouwer degree k (and assume wlog $k>0$). Use $p_1,...,p_n$ to denote elements of $f^{-1}(p)$ and use $q_1,.. …
- 6,546
15
votes
Accepted
Is an inextensible manifold necessarily compact?
Yes, $M$ must be compact. In fact, if $M$ is non-compact, it admits a non-surjective self embedding $f:M\rightarrow M$.
When $n=1$, the only non-compact manifold is $\mathbb{R}$, which obviously admi …
- 6,546
3
votes
Accepted
Smoothness of frame bundle of (global) orbifolds [reference request]
First, one can clearly assume $M$ is connected by simply applying the argument to each componenet of $M$.
The key fact is a generalization of your argument for $M=\mathbb{R}^n$: that if $f:M\rightarr …
- 6,546