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I would like to ask for some detailed reference for quantum Teichmuller theory, better in a mathematical taste. I read a little bit on Kashaev's or Chekhov and Fock's, but find that I need to fill lots of details when I try to proceed. I would like to ask wether there are some good reference in this area, no matter in differential geometrical manner, topological manner, or algebraic manner. Many thanks.

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  • $\begingroup$ You might want to try this over on Math Overflow. $\endgroup$
    – eyeballfrog
    Commented Oct 26, 2018 at 0:46

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I would recommend:

  1. Part D of "Handbook of Teichmueller theory, Volume 1", edited by Athanase Papadopoulos.
  2. Lectures on quantum Teichmueller theory, by Rinat Kashaev (School on quantum topology and geometry, Tolouse, 2017): http://www.cimi.univ-toulouse.fr/inv3d/sites/default/files/atoms/files/lecture_notes-rinatkashaev-notes_by_nezhlaaghaee.pdf
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