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In Hatcher, Allen; Lochak, Pierre; Schneps, Leila, On the Teichmüller tower of mapping class groups, J. Reine Angew. Math. 521, 1-24 (2000). ZBL0953.20030) pages 13 and 15 we have :

for case "d" and "e"we have following diagram (shapes right) :

enter image description here

why these are diagrams for "d" and "e" ? i can't understand how we can get this diagram ?

i think we have following relation and shape for "d" and "e":

enter image description here

are my pictures true ? how we can get diagrams for "d" and "e" ?

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  • $\begingroup$ You need to supply more information if you want a response. i.e. I don't think many readers will download a paper to find your example. $\endgroup$
    – Ryan Budney
    Jun 20, 2022 at 2:41
  • $\begingroup$ @RyanBudney .There are sixteen possible configurations of three saddles on one level, shown in figure 10 of paper, where the saddles are regarded as 1-handles, or rectangles, attached to level curves. The sixteen configurations are grouped into eight pairs, the two configurations in each pair being related by replacing $f_{tu}$ by its negative. $$ f_{t u}(x, y)=\pm x^{4} \pm\left(u-u_{0}\right) x^{2} \pm\left(t-t_{0}\right) x \pm y^{2} $$ $\endgroup$
    – 1200785626
    Jun 20, 2022 at 3:26

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