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Results tagged with manifolds
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user 99732
A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
21
votes
1
answer
745
views
Is $\mathbb{CP}^3$ minus two points the universal cover of a compact manifold?
After reading some recent questions on mathoverflow about universal coverings, I am curious about the following:
Is it possible to construct a closed $6$-manifold $M$, with universal cover homeomorphi …
- 6,995
14
votes
1
answer
494
views
3-fold of general type homeomorphic to rational 3-fold
Is there a smooth (complex projective) 3-fold of general type which is homeomorphic (in the complex topology) to a rational $3$-fold?
I am aware of such examples in complex dimension $2$, for exampl …
- 6,995
8
votes
1
answer
393
views
Universal cover with one end
Suppose that $M$ is a non-compact manifold of finite topological type with one end which is the universal cover of some closed manifold $N$.
Is $M $ necessarily homeomorphic to the total space of some …
- 6,995
3
votes
0
answers
86
views
non-smooth manifold with circle action (with fixed points)
I am interested to know if there a non-smooth manifold (i.e. a closed topological manifold admitting no smooth structure) $M$, having a continuous action $M \times S^1 \rightarrow M$, and the number o …
- 6,995