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There are many results mentioned pairs of pants, and it seems to be a classical model. Why are the pairs of pants so useful?

For example, does it have any application if we estimate the perimeter or the volume of hyperbolic pairs of pants?

Thanks.

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  • $\begingroup$ This seems quite broad, as it underlies all the theory of hyperbolic surfaces... the question "what special structure..." is quite vague too. One introductory book with emphasis on pants is "Geometry and spectra of Riemann surfaces" by P. Buser. $\endgroup$
    – YCor
    Commented Oct 21, 2018 at 10:05
  • $\begingroup$ The question is quite broad as well as regards the number of puns it can generate... $\endgroup$
    – YCor
    Commented Oct 21, 2018 at 10:11
  • $\begingroup$ @YCor Thanks a lot for your suggestion. I’ve edited the question, though I’m not sure if it can make the question better... $\endgroup$
    – user117580
    Commented Oct 21, 2018 at 10:33
  • $\begingroup$ Key words to search for are Fenchel-Nielsen coordinates, which are global parameters for the Teichmuller space of a surface, expressed in terms of a chosen pair of pants decomposition of that surface. $\endgroup$
    – Lee Mosher
    Commented Oct 21, 2018 at 16:53

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