The Kauffman bracket skein module of the connected sum of two genus-one handlebodies is determined over Z[q^{±1}].
Quantum traces for representations of surface groups in SL_2
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
We consider two different quantizations of the character variety consisting of all representations of surface groups in SL_2. One is the skein algebra considered by Przytycki-Sikora and Turaev. The other is the quantum Teichmuller space introduced by Chekhov-Fock and Kashaev. We construct a homomorphism from the skein algebra to the quantum Teichmuller space which, when restricted the classical case, corresponds to the equivalence between these two algebras through trace functions.
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
-
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}].
-
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.