The topological-manifolds tag has no wiki summary.

**19**

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**1**answer

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### good covers of manifolds

It is well-known and easy to prove (see for instance this post) that every smooth manifold admits a "good cover", i.e. a locally finite cover by open balls such that all nonempty intersections of the ...

**3**

votes

**2**answers

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### The group of diffeomorphisms with compact support

Let $M$ be a topological/differentiable manifold. Is there any topology on the group of homeomorphisms/diffeomorphisms with compact support, turning it into a (locally-)compact topological group?
(My ...

**6**

votes

**1**answer

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### How can gauge theory techniques be useful to study when topological manifolds can be triangulated?

I was reading a review article arXiv:1310.7644 and it was explained there that in the last few years it was proven that there are topological manifolds of dimension greater than four that cannot be ...

**13**

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**3**answers

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### Does a *topological* manifold have an exhaustion by compact submanifolds with boundary?

If $M$ is a connected smooth manifold, then it is easy to show that there is a sequence of connected compact smooth submanifolds with boundary $M_1\subseteq M_2\subseteq\cdots$ such that ...

**10**

votes

**1**answer

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### orbit space of a topological manifold

Given a compact Lie group G acting freely on a topological manifold M, is it true that the orbit space M/G is also a topological manifold? If so, why?

**17**

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**0**answers

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### When is a compact topological 4-manifold a CW complex?

Freedman's $E_8$-manifold is nontriangulable, as proved on page (xvi) of the Akbulut-McCarthy 1990 Princeton Mathematical Notes "Casson's invariant for oriented homology 3-spheres".
Kirby showed that ...