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Results tagged with differential-topology
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user 32022
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”.
13
votes
Accepted
On the state of the art on closed $(n-1)$-connected $2n$ manifolds
The classification problem of smooth oriented closed $(n-1)$-connected $2n$-manifolds for $n\ge3$ splits into three parts.
Classify smooth almost closed compact oriented $(n-1)$-connected $2n$-manifo …
- 2,974
4
votes
Accepted
Version of pseudo-isotopy $\neq$ isotopy for $(n+1)$-framings
Take any pseudoisotopy $\varphi\colon M\times I\rightarrow M\times I$ from the identity to a diffeomorphism $\phi$ that is not isotopic to the identity (as you mentioned, these exist). By obstruction …
- 2,974
18
votes
1
answer
1k
views
Is the restriction map for embeddings of manifolds with boundary a fibration?
Let $M$ and $W$ be smooth manifolds (possibly with boundary) and $V\subseteq W$ a submanifold. We have a map between embedding spaces
$$Emb(W,M)\rightarrow Emb(V,M)$$ given by restriction.
Richard Pa …
- 2,974
14
votes
2
answers
2k
views
Reference Request: Compact manifolds with boundary have the homotopy type of a CW-complex
Let $M$ be a compact manifold (possibly non-smooth) manifold with boundary $\partial M$.
Is the inclusion $\partial M\hookrightarrow M$ homotopy equivalent to the inclusion of a subcomplex into a CW- …
- 2,974