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6 Gauthier withdrawal

Edit: I think LMO is correct. Massuyeau has a nice explanation here.
Edit: Renaud Gauthier has retracted the claim of an error in the foundations of the LMO construction, and has withdrawn both preprints from arXiv.

Original post follows:

In two papers posted to the arXiv in the past few days, Renaud Gauthier claims to have discovered an error in the definition of the framed Kontsevich integral used in the construction of the LMO invariant. I have no reason to doubt him. I looked at these papers some years back and recall that something funny was going on with the normalization under handle-slides. I got the wrong multiple of the normalization factor $\nu$, just as Gauthier does. Gauthier fixes the normalization so that it works, but then remarks that subsequent results depending on this construction need to be carefully checked.

My question is whether anyone knows of results that use the fine details of the definition of the framed Kontsevich integral (or LMO invariant or Aarhus integral) which are now thrown into doubt because of this error.

Edit: Here are links to the papers.

On the foundations of the LMO invariant

On the LMO Invariant, the Wheeling Theorem, and the Aarhus Integral

Edit 2: Moskovich has started a blog post on this. Thanks to Ryan Budney for pointing this out.

A problem with LMO?

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Edit: I no longer believe Gauthier's result think LMO is plausible. At the bottom of p.59 of his first preprint, to realize an isotopy he cancels two pairs of critical points, which exactly accounts for the $\nu^2$ that he claims shouldn't be therecorrect. This was the crux of his claim that there is an error in LMOMassuyeau has a nice explanation here.

Original post follows:

In two papers posted to the arXiv in the past few days, Renaud Gauthier claims to have discovered an error in the definition of the framed Kontsevich integral used in the construction of the LMO invariant. I have no reason to doubt him. I looked at these papers some years back and recall that something funny was going on with the normalization under handle-slides. I got the wrong multiple of the normalization factor $\nu$, just as Gauthier does. Gauthier fixes the normalization so that it works, but then remarks that subsequent results depending on this construction need to be carefully checked.

My question is whether anyone knows of results that use the fine details of the definition of the framed Kontsevich integral (or LMO invariant or Aarhus integral) which are now thrown into doubt because of this error.

Edit: Here are links to the papers.

On the foundations of the LMO invariant

On the LMO Invariant, the Wheeling Theorem, and the Aarhus Integral

Edit 2: Moskovich has started a blog post on this. Thanks to Ryan Budney for pointing this out.

A problem with LMO?

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# Propagation of an error in the LMO invariant? (Revision:Idon'tthinkLMOiswrong!)

Edit: I no longer believe Gauthier's result is plausible. At the bottom of p.59 of his first preprint, to realize an isotopy he cancels two pairs of critical points, which exactly accounts for the $\nu^2$ that he claims shouldn't be there. This was the crux of his claim that there is an error in LMO.

Original post follows:

In two papers posted to the arXiv in the past few days, Renaud Gauthier claims to have discovered an error in the definition of the framed Kontsevich integral used in the construction of the LMO invariant. I have no reason to doubt him. I looked at these papers some years back and recall that something funny was going on with the normalization under handle-slides. I got the wrong multiple of the normalization factor $\nu$, just as Gauthier does. Gauthier fixes the normalization so that it works, but then remarks that subsequent results depending on this construction need to be carefully checked.

My question is whether anyone knows of results that use the fine details of the definition of the framed Kontsevich integral (or LMO invariant or Aarhus integral) which are now thrown into doubt because of this error.

Edit: Here are links to the papers.

On the foundations of the LMO invariant

On the LMO Invariant, the Wheeling Theorem, and the Aarhus Integral

Edit 2: Moskovich has started a blog post on this. Thanks to Ryan Budney for pointing this out.

A problem with LMO?

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