Timeline for What are the open subsets of $\mathbb{R}^n$ that are diffeomorphic to $\mathbb{R}^n$
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| S Dec 28, 2020 at 17:20 | history | suggested | ABIM | CC BY-SA 4.0 |
prettied notation
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| Dec 28, 2020 at 16:03 | review | Suggested edits | |||
| S Dec 28, 2020 at 17:20 | |||||
| Nov 7, 2009 at 1:19 | comment | added | Ryan Budney | Yeah, I think the argument goes like this: if its simply-connected at infinity, you apply Larry Siebenmann's dissertation to find a manifold compactification. Contractibility tells you this compactification is a topological n-ball. This argument requires a dimension restriction to n >= 6 though. | |
| Nov 7, 2009 at 1:11 | comment | added | j.c. | en.wikipedia.org/wiki/Simply_connected_at_infinity claims that contractibility and simple connectedness at infinity are equivalent to being homeomorphic to R^n. So I guess the results described in the page I linked to above go both ways after all. | |
| Nov 7, 2009 at 1:00 | comment | added | j.c. | Following up on Ryan Budney's response, there's some discussion of subsets of R^n which are homeomorphic to R^n here: math.niu.edu/~rusin/known-math/95/contractible . Contractibility is not enough, but I don't think any full necessary and sufficient conditions are given in that thread. | |
| Nov 7, 2009 at 0:43 | history | answered | Ryan Budney | CC BY-SA 2.5 |