scholarly journals A survey of quantum Teichmüller space and Kashaev algebra

2014 ◽  
pp. 759-784
Author(s):  
Ren Guo
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space ◽  
Quantum Teichmüller Space ◽  
Quantum Teichmuller Space

scholarly journals A quantum Teichmüller space

1999 ◽  
Vol 120 (3) ◽  
pp. 1245-1259 ◽  
Author(s):  
V. V. Fock ◽  
L. O. Chekhov
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space ◽  
Quantum Teichmüller Space ◽  
Quantum Teichmuller Space

scholarly journals THE QUANTUM TEICHMÜLLER SPACE AS A NONCOMMUTATIVE ALGEBRAIC OBJECT

2009 ◽  
Vol 18 (05) ◽  
pp. 705-726 ◽  
Author(s):  
XIAOBO LIU
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space ◽  
Algebraic Functions ◽  
3 Dimensional ◽  
Quantum Teichmüller Space ◽  
Quantum Teichmuller Space

We consider the quantum Teichmüller space of the punctured surface introduced by Chekhov–Fock–Kashaev, and formalize it as a noncommutative deformation of the space of algebraic functions on the Teichmüller space of the surface. In order to apply it in 3-dimensional topology, we put more attention to the details involving small surfaces.

scholarly journals QUANTUM TEICHMÜLLER SPACES AND QUANTUM TRACE MAP

2017 ◽  
Vol 18 (2) ◽  
pp. 249-291 ◽  
Author(s):  
Thang T. Q. Lê
Keyword(s):  
Teichmüller Space ◽  
Teichmuller Space ◽  
Skew Field ◽  
Trace Map ◽  
Teichmuller Spaces ◽  
Kauffman Bracket ◽  
Quantum Teichmüller Space ◽  
Quantum Teichmuller Space ◽  
Marked Surface ◽  
Natural Way

We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum Teichmüller space of a marked surface, defined by Chekhov–Fock (and Kashaev) in an abstract way, can be realized as a concrete subalgebra of the skew field of the skein algebra.

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