Timeline for A sufficient condition for a space to be an Eilenberg-Maclane space
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 17, 2013 at 6:23 | comment | added | Eric Wofsey | Having looked at Ghrist's argument, it seems that the flaw is in the final sentence: having homotoped the inclusion $K\to C^N(T)$ onto a graph, he claims that graph must be nullhomotopic in $C^N(T)$. This need not be true since that graph might have loops that don't lift to $K$ (which will be the case if $K$ is a Warsaw circle). But I believe the argument does work if you assume $K$ is locally path-connected. | |
| Aug 16, 2013 at 23:36 | comment | added | Ricardo Andrade | @Eric: In fact, it appears that you can topologically embed by a non-null map $W\to C^2(T)$ a Warsaw circle $W$ in the space of pairs of distinct points in the tree $T$ given by the cone on three points. Note that $C^2(T)$ has the homotopy type of a circle. | |
| Aug 16, 2013 at 21:47 | answer | added | Eric Wofsey | timeline score: 5 | |
| Aug 16, 2013 at 21:24 | comment | added | Eric Wofsey | Without some additional niceness hypothesis on $K$, I don't believe Ghrist's theorem is true. For instance, for an annulus $X$, there is a simply connected subset $K$ that is not nullhomotopic in $X$ (take a Warsaw circle around the hole). It should be easy to do something similar inside $C^N(T)$. | |
| Aug 16, 2013 at 19:12 | answer | added | Jeff Strom | timeline score: 1 | |
| Aug 16, 2013 at 18:19 | review | First posts | |||
| Aug 16, 2013 at 18:41 | |||||
| Aug 16, 2013 at 18:02 | history | asked | Peter | CC BY-SA 3.0 |