Timeline for How to compute $\pi_{3}$ of $L(p,q)\# L(p',q')$?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 31, 2014 at 12:45 | vote | accept | Haimiao Chen | ||
| Oct 31, 2014 at 12:40 | vote | accept | Haimiao Chen | ||
| Oct 31, 2014 at 12:45 | |||||
| Oct 31, 2014 at 11:41 | answer | added | Fernando Muro | timeline score: 8 | |
| Oct 31, 2014 at 11:14 | comment | added | Fernando Muro | @AlexSuciu OK, somehow I didn't see "the group ring of". | |
| Oct 31, 2014 at 0:10 | comment | added | Alex Suciu | @FernandoMuro: the group ring $\mathbb{Z} G$ of a group $G$ is the free abelian group on $G$ (as a group). | |
| Oct 30, 2014 at 21:08 | answer | added | Allen Hatcher | timeline score: 28 | |
| Oct 30, 2014 at 16:31 | comment | added | Haimiao Chen | @AlexSuciu Thank you. So I know hom complicated the result will be. | |
| Oct 30, 2014 at 16:09 | comment | added | BS. | I assume that the group law is addition. | |
| Oct 30, 2014 at 16:07 | comment | added | Fernando Muro | @AlexSuciu a non-abelian $\pi_2$? | |
| Oct 30, 2014 at 15:51 | comment | added | Alex Suciu | The second homotopy group of $M\# N$ is the group ring of $\pi_1(M)*\pi_1(N)$. Composing with the Hopf map $S^3\to S^2$ yields non-trivial elements of $\pi_3(M\# N)$. When, say, $M$ is a lens space, we also have non-trivial elements of $\pi_3(M\# N)$ coming from $\pi_3(M)=\mathbb{Z}$. | |
| Oct 30, 2014 at 15:30 | review | First posts | |||
| Oct 30, 2014 at 15:47 | |||||
| Oct 30, 2014 at 15:25 | history | asked | Haimiao Chen | CC BY-SA 3.0 |