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W. Veech on Teichmüller curves in moduli space, Eisenstein series and applications to triangular billiards says on the second paragraph of page 579:

"Thurston's original construction [8] corresponds to the case $r=s=1$." In this context [8] refers to a preprint of Thurston. A reference to this preprint can be also found in Thurston's On the geometry and dynamics of diffeomorphisms of surfaces, where he begins by saying "This article was widely circulated as a preprint".

I'm looking for a reference / copy of this preprint. More precisely, for a reference of Thurston's contruction of pseudo-Anosov homeomorphisms using only two curves (which was later generalized to the case of multicurves.

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As you know, the preprint was published in the Bulletin of the AMS here. There, at the end of the preface, Thurston writes:

There would be no simple stopping point if I began to incorporate the more recent developments in the original paper, so it is being published here in the original form.

I do not possess a scanned copy of the preprint version to check, but based on this quote, I would not expect that there are any significant differences.

One source that should be mentioned in this connection is "Travaux de Thurston sur les surfaces" by Fathi, Laudenbach and Poénaru, Astérisque, vols. 66–67, 1979 (it is cited in Veech's paper as reference 0 and as [FLP] in the preface mentioned above). It is a detailed exposition of the results sketched in Thurston's short paper; in particular, Exposé 13 discusses Thurston's construction of pseudo-Anosov homeomorphisms via Dehn twists. An English translation by Kim and Margalit (titled "Thurston's work on surfaces") was published in 2012.

Incidentally, here is a review in the Bulletin of the AMS by Margalit (of the translation); it gives many more references to follow-up work.

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  • $\begingroup$ @Francois Ziegler, thanks for pointing out that out. I indeed misread the intent of the question, so I have clarified my answer. $\endgroup$
    – j.c.
    Commented Oct 12, 2018 at 13:52
  • $\begingroup$ Ha. I started just moving the link (see history) but your edit is better. It’s all good. $\endgroup$
    – Francois Ziegler
    Commented Oct 12, 2018 at 13:56
  • $\begingroup$ Thanks for the answers. Maybe what confused me is Veech's phrase (I should have pointed that one too): "We now extend a devide of Thurston's [8] to reverse the discussion above and produce examples. Thurston informs us he has made a similar extension." five lines after (9.7) page 578. Since [8] is the preprint, I thought there was an earlier version of [8] which differed from the published paper and which didn't consider the case of multicurves. $\endgroup$
    – Ferran V.
    Commented Oct 13, 2018 at 2:30

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