Timeline for Toral rank conjecture
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 10, 2015 at 15:59 | comment | added | MyIsmail | @MarkGrant : Yes ideed the inequality is: $\dim H^∗(X;\mathbb Q)\geq \frac 12(r^2+r)$. | |
| Apr 3, 2015 at 17:10 | comment | added | Mark Grant | @MyIsmail: I think the $2$ in the second bound should be $1/2$. | |
| Mar 31, 2015 at 10:08 | comment | added | MyIsmail | I'v found the following: Aman showed in 2012 see arXiv:1204.6276 that $$\dim H^*(X;\mathbb Q)\geq 2(r+[r/3]).$$ 20 years before, Hilali proved in 1990 (see Theorem D) that $$\dim H^*(X;\mathbb Q)\geq 2(r^2+r).$$ | |
| Mar 28, 2015 at 8:03 | comment | added | MyIsmail | Yes, TRC is ok for $rk_0(X)\leq 3$. For $rk_0(X)\geq 3$, Puppe bounded the rational cohomological dimension by 2(r+1). Is there any other best approximation? | |
| Mar 27, 2015 at 21:05 | comment | added | Dietrich Burde | Yes, thank you. Ustionovsky says $m\le 3$, right ? | |
| Mar 27, 2015 at 21:02 | history | edited | Dietrich Burde | CC BY-SA 3.0 |
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| Mar 27, 2015 at 20:47 | comment | added | MyIsmail | Thanks Dietrich. Just note that following both USTIONOVSKY introduction and Puppe Theorem 1.1, the rational TRC is resolved for $rk_0(X)\geq 3$. | |
| Mar 27, 2015 at 20:31 | history | answered | Dietrich Burde | CC BY-SA 3.0 |