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Results tagged with differential-topology
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user 25511
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”.
8
votes
1
answer
699
views
Immersion of $S^1$ in $\mathbb{R}^2$ that can be extended to $\mathbb{D}$
I was wondering about $\mathcal{C}^{\infty}$ immersions $S^1 \longrightarrow \mathbb{R}^2$ which are the restriction to $\partial \mathbb{D}$ of an immersion $\overline{\mathbb{D}} \longrightarrow \m …
- 2,696
26
votes
6
answers
3k
views
How to get convinced that there are a lot of 3-manifolds?
My question is rather philosophical : without using advanced tools as Perlman-Thurston's geometrisation, how can we get convinced that the class of closed oriented $3$-manifolds is large and that simp …
- 2,696