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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 4th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexthe idea and some references <a href="https://ncatlab.org/nlab/revision/the+little+n-disk+operad+is+formal/1">v1</a>, <a href="https://ncatlab.org/nlab/show/the+little+n-disk+operad+is+formal">current</a>

   the idea and some references

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 4th 2018
   • (edited Nov 4th 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexIn [Campos-Willwacher 16](https://ncatlab.org/nlab/show/graph+complex#CamposWillwacher16) and followups, the authors highlight that the quasi-iso from the graph complex to the de Rham complex of configuration spaces _sends edges to AKSZ-model Feynman propagators_, hence that those differential forms "$g_{i j}$" pulled back from the boundary spheres of the FM-compactification are essentially to be identified with the Feynman propagators of some (any?) AKSZ sigma-model. This sounds quite plausible, but has this been made precise? Campos-Willwacher seem to indicate that the details for this claim are implicit in articles by Alberto Cattaneo and coauthors. This sounds also rather plausible! But where exactly? Where in the literature would this claim have been substantiated, that the quasi-iso from graph complexes to de Rham complexes of configuration spaces sends edges to AKSZ Feynman propagators? (I have emailed Alberto about it. But if anyone has any insight otherwise, let me know.)

   In Campos-Willwacher 16 and followups, the authors highlight that the quasi-iso from the graph complex to the de Rham complex of configuration spaces sends edges to AKSZ-model Feynman propagators, hence that those differential forms “$g_{i j}$” pulled back from the boundary spheres of the FM-compactification are essentially to be identified with the Feynman propagators of some (any?) AKSZ sigma-model.

   This sounds quite plausible, but has this been made precise? Campos-Willwacher seem to indicate that the details for this claim are implicit in articles by Alberto Cattaneo and coauthors. This sounds also rather plausible!

   But where exactly? Where in the literature would this claim have been substantiated, that the quasi-iso from graph complexes to de Rham complexes of configuration spaces sends edges to AKSZ Feynman propagators?

   (I have emailed Alberto about it. But if anyone has any insight otherwise, let me know.)

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 4th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexah, probably this here: Remark 3.6 in * [[Raul Bott]], [[Alberto Cattaneo]], _Integral invariants of 3-manifolds_, J. Diff. Geom., 48 (1998) 91-133 ([arXiv:dg-ga/9710001](https://arxiv.org/abs/dg-ga/9710001)) re-amplified as remark 11 in * [[Alberto Cattaneo]], [[Pavel Mnev]], _Remarks on Chern-Simons invariants_, Commun.Math.Phys.293:803-836,2010 ([arXiv:0811.2045](https://arxiv.org/abs/0811.2045))

   ah, probably this here:

   Remark 3.6 in

   • Raul Bott, Alberto Cattaneo, Integral invariants of 3-manifolds, J. Diff. Geom., 48 (1998) 91-133 (arXiv:dg-ga/9710001)

   re-amplified as remark 11 in

   • Alberto Cattaneo, Pavel Mnev, Remarks on Chern-Simons invariants, Commun.Math.Phys.293:803-836,2010 (arXiv:0811.2045)
4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 4th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexand these two references really mainly recall the observation of Section 2 of * [[Scott Axelrod]], [[Isadore Singer]], _Chern--Simons Perturbation Theory II_, J. Diff. Geom. 39 (1994) 173-213 ([arXiv:hep-th/9304087](http://arxiv.org/abs/hep-th/9304087)) I am collecting these pointers [here](https://ncatlab.org/nlab/show/Fulton-MacPherson+operad#ReferencesPropagator) at _[[Fulton-MacPherson operad]]_, for the moment, but this should eventually get its own discussion somewhere...

   and these two references really mainly recall the observation of Section 2 of

   • Scott Axelrod, Isadore Singer, Chern–Simons Perturbation Theory II, J. Diff. Geom. 39 (1994) 173-213 (arXiv:hep-th/9304087)

   I am collecting these pointers here at Fulton-MacPherson operad, for the moment, but this should eventually get its own discussion somewhere…

5. • CommentRowNumber5.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMar 30th 2021
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded a reference: The following paper constructs a canonical chain of formality quasiisomorphisms for the operad of chains on framed little disks and the operad of chains on little disks. The construction is done in terms of logarithmic algebraic geometry and is remarkable for being rational (and indeed definable integrally) in de Rham cohomology: * [[Dmitry Vaintrob]], _Formality of little disks and algebraic geometry_, [arXiv:2103.15054](https://arxiv.org/abs/2103.15054). <a href="https://ncatlab.org/nlab/revision/diff/the+little+n-disk+operad+is+formal/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/the+little+n-disk+operad+is+formal/7">v7</a>, <a href="https://ncatlab.org/nlab/show/the+little+n-disk+operad+is+formal">current</a>

   Added a reference:

   The following paper constructs a canonical chain of formality quasiisomorphisms for the operad of chains on framed little disks and the operad of chains on little disks. The construction is done in terms of logarithmic algebraic geometry and is remarkable for being rational (and indeed definable integrally) in de Rham cohomology:

   • Dmitry Vaintrob, Formality of little disks and algebraic geometry, arXiv:2103.15054.

   diff, v7, current