Timeline for A question on composites of pushforward and pullback
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 7, 2013 at 9:21 | comment | added | Russell | @Chris, it looks like I'm wearing my dunce cap tonight, having forgotten that $2 id =0$ in $\mathbb{Z}_{2}$. | |
| Mar 7, 2013 at 9:19 | history | edited | Russell | CC BY-SA 3.0 |
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| Mar 7, 2013 at 8:33 | vote | accept | Juan | ||
| Mar 7, 2013 at 8:48 | |||||
| Mar 7, 2013 at 8:33 | comment | added | Chris Gerig | @Russell, this still doesn't work because $|\mathbb{Z}_2|$ will kill the 2-torsion, and so the conclusion would be satisfied trivially. | |
| Mar 7, 2013 at 8:31 | comment | added | Chris Gerig | @Juan that is not enough, because his original example had $S^{2k}$ orientable while $\mathbb{R}P^{2k}$ is nonorientable! You need a condition on the action (luckily for $S^{2k+1}$ the antipodal action has orientable quotient). | |
| Mar 7, 2013 at 7:49 | history | edited | Russell | CC BY-SA 3.0 |
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| Mar 7, 2013 at 7:46 | comment | added | Juan | Thank you for the answer, Russell. I just added orientability in my question. I would appreciate your counter-example. | |
| Mar 7, 2013 at 7:42 | comment | added | Russell | Ahh, good point! I'll modify the example so that everything is orientable. | |
| Mar 7, 2013 at 7:37 | comment | added | Chris Gerig | Be careful, we're invoking Poincare-duality and so your spaces have to be orientable. I assume the question wants $X$ oriented and $\pi$ to be orientation-preserving. | |
| Mar 7, 2013 at 7:32 | history | answered | Russell | CC BY-SA 3.0 |