Timeline for Lifting criteria of covering space by using homology condition
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Jul 27, 2010 at 16:15 | history | undeleted | Topologieee | ||
| Jul 27, 2010 at 16:14 | history | deleted | Topologieee | ||
| Jul 21, 2010 at 4:02 | comment | added | Torsten Ekedahl | Yes, as $f_*(\pi_1(\tilde X))$ contains commutators and $p$'th powers. | |
| Jul 20, 2010 at 16:46 | comment | added | Topologieee | And I have another question. Is $H_1(X)/\pi_*(H_1(\tilde{X}))=\pi_1(X)/\pi_*(\pi_1(\tilde{X}))$? | |
| Jul 20, 2010 at 16:30 | comment | added | Topologieee | Thank you for your friendly comment. I was only checking algebraic criterion. Geometrically, it seems obvious that $f$ lifts iff $f_*$ preserves $\mathcal{A}$. | |
| Jul 20, 2010 at 15:51 | comment | added | Torsten Ekedahl | $H_1(X;\mathbb Z/p)$ is the fundamental group of $X$ modulo commutators and $p$'th powers. Hence, a cyclic cover of degree $p$ is completely determined by $\mathcal A$. In particular $f$ lifts iff $f_*$ preserves $\mathcal A$. | |
| Jul 20, 2010 at 14:56 | history | edited | Anweshi | CC BY-SA 2.5 |
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| Jul 20, 2010 at 14:51 | history | edited | Topologieee | CC BY-SA 2.5 |
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| Jul 20, 2010 at 14:50 | history | edited | Greg Kuperberg | CC BY-SA 2.5 |
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| Jul 20, 2010 at 14:46 | history | asked | Topologieee | CC BY-SA 2.5 |