Timeline for Hit problem and $\left( \mathbb{F}_2 \otimes_{A} P_6 \right)_{10}$
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 8, 2013 at 8:01 | comment | added | Fernando Muro | I see, $x^2=0$ but higher powers need not be $0$ since you're killing a sub-$A$-bmodule of $P_1$, not an ideal, that's my mistake. | |
| Oct 7, 2013 at 18:08 | comment | added | John Palmieri | Fernando: If $P_1=\mathbb{F}_2[x]$, then $\mathbb{F}_2 \otimes_A P_1$ is spanned by the elements $x^{2^n-1}$. So it's more complicated than that. | |
| Oct 7, 2013 at 16:07 | comment | added | Fernando Muro | I may be horribly mistaken, but if you're killing the action of the Steenrod algebra, you obtain a quotient of the exterior algebra on the same generators, which is trivial above dimension 6, so the answer would be 0. | |
| Oct 7, 2013 at 14:17 | comment | added | John Palmieri | $P_6$ means the cohomology of a 6-fold product of $\mathbf{R}P^\infty$ with itself. Thus it's a polynomial ring on 6 generators, each in degree 1. | |
| Oct 7, 2013 at 12:00 | comment | added | Fernando Muro | I still don't get the degrees | |
| Oct 7, 2013 at 11:55 | comment | added | user69833 | I am sorry. The monomial $x_1^a\dots x_6^f$ with $10=a+ \dots f$. In above fomular, $x$ means $x_i$. | |
| Oct 7, 2013 at 11:52 | review | First posts | |||
| Oct 7, 2013 at 11:53 | |||||
| Oct 7, 2013 at 11:47 | comment | added | Fernando Muro | You mean that for $x= x_1,\dots, x_6$? What's the degree of the $x_i$? | |
| Oct 7, 2013 at 11:45 | comment | added | user69833 | Yes. Let $Sq^j$ be a square operation in Steenrod algebra. We have $$Sq^j(x)=\left\{\begin{matrix} x, \ \ \ \text{if $j=0$,}\\ x^2, \ \ \ \text{if $j=1$,}\\ 0. \ \ \ \text{otherwise.} \end{matrix}\right.$$ And it satisfies the Cartan fomular $$Sq^{n}(fg)=\sum_{i=0}^nSq^i(f)Sq^{n-i}(g).$$ | |
| Oct 7, 2013 at 11:40 | comment | added | Fernando Muro | How is $P_6$ and $A$-module? | |
| Oct 7, 2013 at 11:35 | history | asked | user69833 | CC BY-SA 3.0 |