Timeline for A question on composites of pushforward and pullback
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 7, 2013 at 21:24 | vote | accept | Juan | ||
| Mar 7, 2013 at 10:28 | vote | accept | Juan | ||
| Mar 7, 2013 at 10:28 | |||||
| Mar 7, 2013 at 9:02 | answer | added | Oscar Randal-Williams | timeline score: 3 | |
| Mar 7, 2013 at 8:53 | comment | added | Juan | @ Chris Sorry for my typo but I meant $\pi_!$, not $\pi_*$. Isn't it the transfer map? You are right; the example below is not a counter-eample. | |
| Mar 7, 2013 at 8:46 | comment | added | Chris Gerig | Neither $\pi_*$ nor $\pi^*$ is the transfer (which goes in the opposite direction). And you shouldn't accept Russell's answer yet because it isn't correct -- his 1st attempted counter-example with n even doesn't satisfy your hypotheses, and his 2nd counter-example with n odd vacuously satisfies your conclusion (i.e. is not a counter-example). | |
| Mar 7, 2013 at 8:33 | vote | accept | Juan | ||
| Mar 7, 2013 at 8:48 | |||||
| Mar 7, 2013 at 8:29 | comment | added | Juan | @Chris π∗ should be the transfer map. If my memory serves, one of the equalities in the last line holds. It seems that Russel's example below shows us the latter does not hold in general... | |
| Mar 7, 2013 at 7:53 | comment | added | Chris Gerig | Have you tried just checking definitions at the chain-level?. One thing to quickly note is that we already have transfer maps that satisfy your conclusion. I'm not sure your construction produces the transfer, and so I wouldn't immediately expect your conclusion to hold. (sorry I'm being lazy right now) | |
| Mar 7, 2013 at 7:45 | history | edited | Juan | CC BY-SA 3.0 |
added "orientable"
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| Mar 7, 2013 at 7:44 | comment | added | Juan | Yes, PD stands for the Poincare duality map. | |
| Mar 7, 2013 at 7:32 | answer | added | Russell | timeline score: 0 | |
| Mar 7, 2013 at 6:16 | history | edited | Chris Gerig | CC BY-SA 3.0 |
added 126 characters in body; added 7 characters in body
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| Mar 7, 2013 at 5:09 | comment | added | Sándor Kovács | I would guess $PD$ stands for Poincaré duality | |
| Mar 7, 2013 at 5:05 | comment | added | Spice the Bird | Could you say what $PD_X,PD_Y$ are? | |
| Mar 7, 2013 at 4:18 | history | asked | Juan | CC BY-SA 3.0 |