4 papers
math.GT2026
Quantized Geodesic Lengths for Teichmüller Spaces: Algebraic Aspects
Hyun Kyu Kim
In 1980's H. Verlinde suggested to construct and use a quantization of Teichmüller spaces to construct spaces of conformal blocks for the Liouville conformal field theory. This su…
math.GT2025
Frobenius homomorphisms for stated -skein modules
Hyun Kyu Kim, Thang T. Q. Lê, Zhihao Wang
The stated -skein algebra of a surface is a quantization of the -character variety, and is spanned over…
math.QA2024
Naturality of quantum trace maps for surfaces
Hyun Kyu Kim, Zhihao Wang
The -skein algebra of a punctured surface , studied by Sikora, is an algebra generated by isotopy classes of -webs living in the thickened surface $\ma…
math.QA2024
The Unicity Theorem and the center of the -skein algebra
Hyun Kyu Kim, Zhihao Wang
The -skein algebra of a punctured oriented surface is a quantum deformation of the coordinate algebra of the ${\rm…