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Quantization of Teichm\"uller spaces and the quantum dilogarithm

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arxiv q-alg/9705021 v1 pith:YJV7IJHH submitted 1997-05-27 q-alg math.QA

R.M. Kashaev This is my paper · ORCID
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keywords classgroupmappingsymplecticquantizationquantumspaceteichm
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The Teichm\"uller space of punctured surfaces with the Weil-Petersson symplectic structure and the action of the mapping class group is realized as the Hamiltonian reduction of a finite dimensional symplectic space where the mapping class group acts by symplectic rational transformations. Upon quantization the corresponding (projective) representation of the mapping class group is generated by the quantum dilogarithms.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow

    hep-th 2024-12 conditional novelty 7.0 of 10

    A framework called SymQRG identifies 3D quantum gravity as the symmetry-preserving RG flow of 2D CFTs, realized discretely by U_q(SL(2,R)) 6j symbols.

  2. Anyon Condensation in Virasoro TQFT: Wormhole Factorization

    hep-th 2024-12 conditional novelty 6.0 of 10

    Condensing a diagonal anyon in Virasoro TQFT factorizes wormhole partition functions and produces Liouville CFT on the two boundary surfaces.

  3. Wilson Towers as Local Bulk Fields

    hep-th 2026-07 conditional novelty 5.0 of 10

    A multi-winding Wilson loop in thermal AdS3 is re-expressed as a sum over single-winding Wilson loops, one per multi-trace primary, so a free bulk field becomes a tower of Wilson lines.

  4. Quantized Geodesic Lengths for Teichm\"uller Spaces: Algebraic Aspects

    math.GT 2024-05 unverdicted novelty 5.0 of 10

    Constructs quantized trace-of-monodromy via Bonahon-Wong maps and verifies Teschner recursion plus strong commutation for disjoint loops in Chekhov-Fock quantum Teichmüller theory.

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