Timeline for Extension of the formality theorem?
Current License: CC BY-SA 3.0
6 events
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| Apr 27, 2011 at 12:27 | history | edited | DamienC | CC BY-SA 3.0 |
include a comment; added 35 characters in body
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| Apr 27, 2011 at 12:11 | comment | added | DamienC | Hi Daniel. If your vector fields does only derivates in the odd directions with coefficients depending only on even coordinates, then it seems ot me that in this specific case the corrections to HKR are trivial. Namely, we define the matrix valued 1-form $\Xi$ by $\Xi_i^j=\sum_k\partial_k\partial_iv_ju^k$ (where $u^k$ are coordinates and $v=\sum_j\partial_j$). Now if you split your variables into odd and even ones, and if $v$ the above specific form, then you see that this matrix has non-zero entries only in the right-up block. In particular the trace of any power of it is zero. | |
| Apr 27, 2011 at 2:37 | comment | added | Daniel Pomerleano | I guess if I have interpreted your beautiful formula 9.8 correctly, the answer is "yes"? | |
| Apr 26, 2011 at 23:39 | comment | added | Daniel Pomerleano | Hi Damien, thanks for your great reply! This was the argument I found in my last paragraph(it's great to have a specialist confirming this) I had suspected that the maps f_1 were different than HKR but wasn't able to get started with the calculations. I have a specific case of interest, when my algebra is pure Sullivan e.g is of the form $k[x_1,\ldots,x_n]\otimes \wedge(e_1,\ldots e_m)$ with $v= \sum f_i(x_1,\ldots x_n)d/de_i $ where the variables $x_i$ are even and the $e_i$ are odd Do you know off hand if the map $f_1$ fails to agree with HKR even in this case? | |
| Apr 26, 2011 at 23:32 | vote | accept | Daniel Pomerleano | ||
| Apr 26, 2011 at 7:53 | history | answered | DamienC | CC BY-SA 3.0 |