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The symplectic sum of Gompf and the symplectic cut of Lerman are known to be inverse of each other, in the sense that if you apply one of these first and the other one afterward, you obtain the original space with a symplectic structure which is homotopically equivalent to the starting one.

But is there an explicit proof of this available anywhere in the literature?

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    $\begingroup$ Section 3 of arXiv:1101.4986 does something like what you're asking for. $\endgroup$
    – Mike Usher
    Sep 2, 2014 at 2:38
  • $\begingroup$ Thanks, I finally wrote it myself. At least in one direction, the main point is the Exercise 3.36 of McDuff-Salamon $\endgroup$ Sep 2, 2014 at 18:55

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