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**8**

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**2**answers

192 views

### Isotopy extension theorems

I'm looking for the origins of the isotopy extension theorem in categories other than the smooth category.
Precisely, in the smooth category, the isotopy extension theorem says that if $f : [0,1] ...

**11**

votes

**1**answer

513 views

### Are there non-compact, non-smoothable manifolds?

There do exist manifolds which do not admit any smooth structure at all. But the only examples I've heard of are all compact.
Are there any non-compact, non-smoothable manifolds?

**17**

votes

**1**answer

809 views

### Diffeomorphisms vs homeomorphisms of 3-manifolds

For a smooth 3-manifold $M$, is the natural map from the space of diffeomorphisms of $M$ to the space of homeomorphisms of $M$,
$${\sf Diff}(M) \longrightarrow {\sf Top}(M),$$
a weak homotopy ...