Quantum Traces in Quantum Teichmüller Theory

Abstract

We prove that for the torus with one hole and p greater than or equal to 1 punctures and the sphere with four holes there is a family of quantum trace functions in the quantum Teichmüller space, analog to the non-quantum trace functions in Teichmüller space, satisfying the properties proposed by Chekhov and Fock in their paper "Observables in 3D Gravity and Geodesic Algebras."

References in corpus (1)

• Representations of the quantum Teichmuller space, and invariants of surface diffeomorphisms

Cited by in corpus (6)

• Quantum traces for representations of surface groups in SL_2
• Quantum Teichmüller spaces and quantum trace map
• Strong positivity for the skein algebras of the $4$-punctured sphere and of the $1$-punctured torus
• Laurent positivity of quantized canonical bases for quantum cluster varieties from surfaces
• ${\mathrm{SL}}_2$ quantum trace in quantum Teichmüller theory via writhe
• Quantum duality maps, skein algebras and their ensemble compatibility