Timeline for What homotopy classes can attaching an $E_n$-cell kill?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 26, 2017 at 4:45 | answer | added | Omar Antolín-Camarena | timeline score: 5 | |
| Jul 21, 2017 at 6:08 | vote | accept | Jonathan Beardsley | ||
| Sep 22, 2017 at 19:00 | |||||
| Jul 20, 2017 at 1:05 | comment | added | Jonathan Beardsley | @tyler no worries there's a lot of text up there :) | |
| Jul 20, 2017 at 1:04 | comment | added | Tyler Lawson | I'm sorry, Jon, I didn't read carefully enough. | |
| Jul 19, 2017 at 18:04 | history | edited | Jonathan Beardsley | CC BY-SA 3.0 |
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| Jul 19, 2017 at 17:59 | comment | added | Jonathan Beardsley | Yeah so to be clear, since $\beta$ is also in $\pi_k$, it must be "multiples" by elements in $\pi_0$. | |
| Jul 19, 2017 at 15:12 | comment | added | Jonathan Beardsley | Sorry I'm having a hard time explaining this clearly. But I'm only really interested in things which are in the same degree as $\alpha$. So $\eta$ is not an issue. | |
| Jul 19, 2017 at 15:11 | answer | added | Tom Bachmann | timeline score: 7 | |
| Jul 19, 2017 at 13:48 | comment | added | Tom Bachmann | @TylerLawson: I think he asking the following: if $t \in \pi_k(A)$ maps to zero in $\pi_k(A//\alpha)$, is it then the case that $t = a_0 \alpha$, for some $a_0 \in \pi_0(A)$. (Note that $t$ and $\alpha$ live in the same degree.) Thus $\eta$ is not a counterexample, not sure if brackets might be. | |
| Jul 19, 2017 at 13:03 | comment | added | Tyler Lawson | Unfortunately not. For example, I'd expect that killing off $x$ also kills off brackets like $\langle x,y,z \rangle$ which may not be multiples of $x$ in homotopy. As another example, killing off 2 in the sphere spectrum in an $E_1$ way also kills the Hopf map $\eta$. | |
| Jul 18, 2017 at 20:46 | history | edited | Jonathan Beardsley | CC BY-SA 3.0 |
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| Jul 18, 2017 at 20:33 | history | asked | Jonathan Beardsley | CC BY-SA 3.0 |