The Kauffman bracket skein module of the connected sum of two genus-one handlebodies is determined over Z[q^{±1}].
Quantization of Teichm\"uller spaces and the quantum dilogarithm
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
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.
fields
math.GT 2verdicts
UNVERDICTED 2representative citing papers
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.
citing papers explorer
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Kauffman bracket skein module of the connected sum of two solid tori
The Kauffman bracket skein module of the connected sum of two genus-one handlebodies is determined over Z[q^{±1}].
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Quantized Geodesic Lengths for Teichm\"uller Spaces: Algebraic Aspects
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.