Timeline for non-simple local coefficient system on a fibration of classifying spaces
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2017 at 1:07 | comment | added | Tom Goodwillie | In general in such an "associated bundle with fiber $F$" the action of $\pi_1 BG=\pi_0G$ on homology of the fiber $F$ is given by the given action of $G$ on $F$. | |
| Nov 3, 2017 at 1:06 | comment | added | Tom Goodwillie | You can think of $G/H\to BH\to BG$ as a special case of the associated bundle for an action of $G$ on a space $F$, $F\to EG\times_G F\to BG$. Let $F$ be $G/H$ with the action I mentioned. Then the bundle is $G/H\to EG\times_G(G/H)\to BG$, where $G\times_G(G/H)=(EG)/H\sim BH$. | |
| Nov 3, 2017 at 0:46 | comment | added | C. Zhihao | Would you mind to illustrate a little bit why the action becomes what you say? it isn't that clear for me | |
| Nov 2, 2017 at 22:04 | answer | added | Nicholas Kuhn | timeline score: 4 | |
| Nov 2, 2017 at 21:56 | comment | added | Tom Goodwillie | The element of $\pi_1(BG)=\pi_0(G)$ represented by $g\in G$ acts on the homology of $G/H$ by the map $xH\mapsto gxH$ from $G/H$ to $G/H$.This can be nontrivial. | |
| Nov 2, 2017 at 20:45 | review | First posts | |||
| Nov 2, 2017 at 21:06 | |||||
| Nov 2, 2017 at 20:43 | history | asked | C. Zhihao | CC BY-SA 3.0 |