Timeline for Truncations of E_infinity algebras
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 3, 2020 at 16:03 | comment | added | Maxime Ramzi | But that would imply that $ku\wedge H\mathbb Z$ is also rational, which it's not (2/2) | |
| Dec 3, 2020 at 16:03 | comment | added | Maxime Ramzi | @TylerLawson : I think it's not true that $\tau_{\leq 0}KU\wedge \tau_{\leq 0}KU$ is rational; but the example still works (if $\tau_{\leq 0}KU$ had a ring structure it would be a module over its $\pi_0$, i.e. an Eilenberg-MacLane spectrum; but its $k$-invariants are the same as those of $KU$, so it's not an EM spectrum). The reason I think it's not rational is because $KU\wedge \tau_{\leq 0}KU$ is rational (it's a homotopy colimit of extensions of $KU\wedge H\mathbb Z$ which is rational), and so it would imply that $ku\wedge \tau_{\leq 0}KU$ is also rational. (1/2) | |
| Apr 10, 2014 at 16:42 | comment | added | Tyler Lawson | Whoops. Yes, that's a ridiculous mistake, I did mean $u \cdot u^{-1} = 1$. | |
| Apr 10, 2014 at 16:32 | vote | accept | user49450 | ||
| Apr 10, 2014 at 16:31 | comment | added | user49450 | I assume you mean $u \cdot u^{-1} = 1$ in the relation? In any case, thank you! I was indeed wondering about compatible $E_\infty$-structures, so your example is wonderful. (And I feel stupid!) | |
| Apr 10, 2014 at 16:26 | history | answered | Tyler Lawson | CC BY-SA 3.0 |