Timeline for When is the one-point compactification well-pointed?
Current License: CC BY-SA 3.0
11 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 2, 2013 at 2:06 | comment | added | Ricardo Andrade | @John: Forward tameness appears to be a useful condition. Nevertheless, I was hoping for a more general criterion. For example, the Whitehead manifold I mentioned above is not forward tame. | |
| Aug 1, 2013 at 23:21 | comment | added | John Klein | I just looked again at Hughes & Ranicki's book. It seems that they give an answer in their setting: Prop 7.11 states that a "forward tame" ANR $W$ has the homotopy type of a based CW complex. | |
| Aug 1, 2013 at 21:36 | comment | added | Ian Agol | I believe a necessary condition is that the space of ends must be discrete. en.wikipedia.org/wiki/End_of_a_space | |
| Aug 1, 2013 at 9:28 | comment | added | Ricardo Andrade | Here is an example which I find counter-intuitive, and may be interesting to keep in mind. The Whitehead manifold is a space with a highly non-trivial topology at infinity whose one-point compactification is nevertheless well-pointed. See this answer by Sergey Melikhov for an explanation. | |
| Aug 1, 2013 at 0:19 | comment | added | John Klein | @ViditNanda: I looked at the paper you suggested, but I am not a shape theorist, so I couldn't make any sense of it. The only statement I could understand was the acknowledgement: "We completed this work during compulsory military service at Military High School in Belgrade. We thank superior officers for providing conditions stimulating research." Could you please tell me where I would find the answer to my question in this paper? | |
| Jul 31, 2013 at 23:27 | comment | added | Vidit Nanda | Have you seen the 1978 paper "Homotopy properties of LC spaces at infinity - smoothness and calmness" by Zvonko Cerin? It's been a while, but I think a more general question is answered there: projecteuclid.org/…. | |
| Jul 31, 2013 at 22:53 | comment | added | John Klein | Oh, that's fine. The more tags the merrier. | |
| Jul 31, 2013 at 22:51 | comment | added | Ricardo Andrade | I added the tag 'gn.general-topology'. Feel free to remove it if you don't think it applies. The tag 'gt.geometric-topology' may also be relevant (but may not be directly applicable). | |
| Jul 31, 2013 at 22:41 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
added tag which seems appropriate
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| Jul 31, 2013 at 22:28 | history | asked | John Klein | CC BY-SA 3.0 |