Timeline for Contraction of graded vector fields on de Rham complex
Current License: CC BY-SA 3.0
5 events
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| Mar 8, 2013 at 18:25 | comment | added | Theo Johnson-Freyd | Sorry, that was a typo. I meant that to speak about $d_{dR}$, you need to say how it's supposed to have bidegree $(0,1)$. What I should have written was $d_{dR} : L_{(0,1)} \otimes \Omega^\bullet \to \Omega^\bullet$. But if you and I disagree about which the generating line in degree $(0,1)$ is (and in particular don't choose an isomorphism between them) then we will each have a $d_{dR}$, and no way to compare them, except that in any fixed skeletalization they'll differ by some scalar. | |
| Mar 8, 2013 at 15:31 | comment | added | dhagbert | Inconsequential nit-pick. Shouldn't you have $\iota_{X}(\alpha \wedge \beta)=\iota_{X}(\alpha) \wedge \beta + (-1)^{mp-q}\alpha \wedge \iota_{X}(\beta)$ rather than Inconsequential nit-pick. Shouldn't you have $\iota_{X}(\alpha \wedge \beta)=\iota_{X}(\alpha) \wedge \beta + (-1)^{mp+q}\alpha \wedge \iota_{X}(\beta)$? Of course, it doesn't matter in the end. | |
| Mar 8, 2013 at 9:09 | comment | added | dhagbert | I'm sorry if it could be interpreted as a slight. It was meant as an invitation for a diversity of answers. Thank you for this very nice answer. One thing about which I'm unclear. You say that the de Rham derivation determines a line object $L_{(0,1)}$. But the source of the differential is the cdga $A$, which is a line in $A$-dg-modules, but not in bigraded vector spaces. | |
| Mar 8, 2013 at 9:03 | vote | accept | dhagbert | ||
| Mar 8, 2013 at 9:06 | |||||
| Mar 8, 2013 at 7:34 | history | answered | Theo Johnson-Freyd | CC BY-SA 3.0 |