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We describe the action of the Kauffman bracket skein algebra on some vector spaces that arise as relative Kauffman bracket skein modules of tangles in the punctured torus. We show how this action determines the Reshetikhin-Turaev representation of the punctured torus. We rephrase our results to describe the quantum group quantization of the moduli space of flat SU(2)-connections on the punctured torus with fixed trace of the holonomy around the boundary.
Jea-Pil Cho, and Răzvan Gelca. "Representations of the Kauffman bracket skein algebra of the punctured torus." Fundamenta Mathematicae 225.0 (2014): 45-55. <http://eudml.org/doc/283161>.
@article{Jea2014, abstract = {We describe the action of the Kauffman bracket skein algebra on some vector spaces that arise as relative Kauffman bracket skein modules of tangles in the punctured torus. We show how this action determines the Reshetikhin-Turaev representation of the punctured torus. We rephrase our results to describe the quantum group quantization of the moduli space of flat SU(2)-connections on the punctured torus with fixed trace of the holonomy around the boundary.}, author = {Jea-Pil Cho, Răzvan Gelca}, journal = {Fundamenta Mathematicae}, keywords = {Kauffman bracket; skein modules; moduli spaces of connections}, language = {eng}, number = {0}, pages = {45-55}, title = {Representations of the Kauffman bracket skein algebra of the punctured torus}, url = {http://eudml.org/doc/283161}, volume = {225}, year = {2014}, }
TY - JOUR AU - Jea-Pil Cho AU - Răzvan Gelca TI - Representations of the Kauffman bracket skein algebra of the punctured torus JO - Fundamenta Mathematicae PY - 2014 VL - 225 IS - 0 SP - 45 EP - 55 AB - We describe the action of the Kauffman bracket skein algebra on some vector spaces that arise as relative Kauffman bracket skein modules of tangles in the punctured torus. We show how this action determines the Reshetikhin-Turaev representation of the punctured torus. We rephrase our results to describe the quantum group quantization of the moduli space of flat SU(2)-connections on the punctured torus with fixed trace of the holonomy around the boundary. LA - eng KW - Kauffman bracket; skein modules; moduli spaces of connections UR - http://eudml.org/doc/283161 ER -