Timeline for Map from homotopy sphere with lifting property induces surjections on homotopy groups. Is it weak equivalence?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 4, 2014 at 6:45 | comment | added | Cusp | I am little confused. Is $C$ a given fixed compact set or for any compact set $C$ and $f$ the lift exists? | |
| Aug 3, 2014 at 1:01 | vote | accept | rgnrmllbrg | ||
| Aug 3, 2014 at 0:46 | comment | added | Eric Wofsey | $C$ is not a simplex but the union of the images of the simplices in $X$. In your $S^1$ example, $C$ would be all of $S^1$, which does not lift to $\mathbb{R}$. | |
| Aug 3, 2014 at 0:25 | comment | added | Eric Wofsey | For any $c\in H_n(X)$, there is some compact subset $C\subseteq X$ such that $c$ is in the image of $H_n(C)\to H_n(X)$ (namely, let $C$ be the union of the images of all the simplices appearing in a representative of $c$). The inclusion $C\to X$ lifts to $E$, and hence $c$ also lifts to $H_n(E)$. | |
| Aug 3, 2014 at 0:13 | history | answered | Eric Wofsey | CC BY-SA 3.0 |