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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 13th 2012
• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeDec 13th 2012

What does it mean

This is due to (Kadeishvili) with more explicit constructions due to (Merkulov).

I remind you that Kadeishvili published quite many papers on the subject in 1980-s and 1990-s, certainly beyond what is listed in the entry. I do not believe there is something directly related to the theorem which is not made explicit by him.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeDec 13th 2012

It’s often referred to as the Kadeishvili-Merkulov theorem (for instance here), and that’s how the $n$Lab has been referring to it all along at A-infinity algebra.

What do you want me to do? Remove the pointer to Merkulov?

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeDec 13th 2012
• (edited Dec 13th 2012)

I heard hundred of times of this theorem and never as Kadeishvili-Merkulov’s theorem. Merkulov has written a very late but clear paper which has the advantage of being in English with application to the Kaehler manifolds (but there were already other secondary references at the time). Reference should stay, but the statement that Merkulov has a more explicit version than Kadeishvili does not hold, even for published papers, so that statement has no place there! Kadeishvili even wrote a booklet of almost 100 pages in 1990-s about the topic, all before Merkulov’s paper. In particular, Kadeishvili knew very clearly the relations to Massey products. The 2006 reference which you quote, has results which I think were also well known before (I certainly heard them from a student of Kadeishvili in 2004 as such a fact).

• CommentRowNumber5.
• CommentAuthorzskoda
• CommentTimeDec 13th 2012

I wrote

This is due to (Kadeishvili). A clear English exposition with applications to Kähler manifolds is in (Merkulov).

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeDec 13th 2012

Okay, thanks.

• CommentRowNumber7.
• CommentAuthorjim_stasheff
• CommentTimeDec 14th 2012
Merkulov misght could be appropriate for the Kaehler examples,
but surely not for the main theorem. I strongly agree with Zoran.
And there are plent of clear expositionsf from Kadeishvili up to jsut before Merkulov,
• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeDec 14th 2012
• (edited Dec 14th 2012)

Okay, thanks${}^2$.