quantum Teichmuller Theory wiki で検索した結果下記

https://ncatlab.org/nlab/show/Teichm%C3%BCller+theory
Teichmuller theory nLab
Contents
1. Idea
2. Properties
Complex structure on Teichmuller space
Relation to moduli stack of complex curves / Riemann surfaces
3. Related concepts
4. References

3. Related concepts
Kodaira-Spencer theory
moduli space of curves
Grothendieck-Teichmuller group
quantum Teichmuller theory
p-adic Teichmuller theory
inter-universal Teichmuller theory
Outer space
for version in supergeometry see at super Riemann surface

https://hal.archives-ouvertes.fr/hal-00706331
HAL (フランス)
Handbook of Teichmuller theory, Volume III
Athanase Papadopoulos 1
1 IRMA - Institut de Recherche Mathematique Avancee

https://scholar.google.ae/citations?user=qrso-ksAAAAJ&hl=ja
Rinat Kashaev
Associate Professor of Mathematics, University of Geneva
Quantum TopologyMathematical Physics

Quantization of Teichmuller spaces and the quantum dilogarithm
RM Kashaev
Letters in Mathematical Physics 43 (2), 105-115 引用246 1998年

http://sciencewise.info/resource/Teichm_ller_modular_group/Teichm%C3%BCller_modular_group_by_Wikipedia
ScienceWISE
Mapping class group of a surface
From Wikipedia, the free encyclopedia
In mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmuller modular group, is the group of homeomorphisms of the surface viewed up to continuous (in the compact-open topology) deformation. It is of fundamental importance for the study of 3-manifolds via their embedded surfaces and is also studied in algebraic geometry in relation to moduli problems for curves.

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