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Results tagged with differential-topology
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user 32487
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”.
4
votes
1
answer
439
views
Is a manifold-with-boundary with given interior and non-empty boundary essentially unique?
Let $M$ be a compact connected manifold-with-boundary such that $\circ M \neq \emptyset$, where $\circ M$ is the boundary of $M$. Let $N$ be a compact connected manifold-with-boundary such that $\circ …
- 397
5
votes
2
answers
551
views
Collared boundary of a non-metrizable manifold
For this question a manifold-with-boundary is a topological space which is Hausdorff and locally upper-Euclidean. Every metrizable manifold-with-boundary has a collared boundary, as shown in "Locally …
- 397
1
vote
Collared boundary of a non-metrizable manifold
Mathieu Baillif provided an answer to the question. I'll leave here some more notes for future readers. The following strengthening of the theorem in Gauld's book "Non-metrizable manifolds" holds:
Le …
- 397