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Results tagged with at.algebraic-topology
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user 428
Homotopy theory, homological algebra, algebraic treatments of manifolds.
34
votes
Are there two non-homotopy equivalent spaces with equal homotopy groups?
$S^3 \times \mathbb{R}P^2$ and $\mathbb{R}P^3 \times S^2$ are both smooth 5-manifolds with fundamental group $\mathbb{Z}/2$ and universal cover $S^3 \times S^2$, so their homotopy groups are all the s …
- 6,589
30
votes
Accepted
Are there non-compact, non-smoothable manifolds?
The Cairns-Hirsch theorem says that a PL manifold $M$ is smoothable if and only if $M\times \mathbb{R}$ is smoothable, so you can take $M$ to be any one of the known compact, PL examples such as Kerva …
- 6,589