Timeline for Homology of the universal cover
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 14, 2019 at 10:15 | comment | added | GSM | @BenWieland How? could you say more, please ? | |
| Jun 13, 2019 at 22:11 | comment | added | Ben Wieland | Oh, yeah. But it would work if the fundamental group were acyclic... | |
| Jun 13, 2019 at 2:22 | comment | added | John Klein | The cofiber of the map $\ast \times S^2 \to S^1 \times S^2$ is $S^1 \wedge (S^2_+) \simeq S^1 \vee S^3$ (which is still a finite complex). So $H_\bullet(X) \neq H_\bullet(S^1)$. Moreover it's clear from this that $\tilde X$ is homotopy equivalent to countable wedge of copies of $S^3$. But your example fails to satisfy condition (3). | |
| Jun 13, 2019 at 1:48 | history | answered | Ben Wieland | CC BY-SA 4.0 |