TY - JOUR
T1 - The action of the Kauffman bracket skein algebra of the torus on the Kauffman bracket skein module of the 3-twist knot complement
AU - Gelca, Rǎzvan
AU - Wang, Hongwei
N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.
PY - 2022/4/1
Y1 - 2022/4/1
N2 - We determine the action of the Kauffman bracket skein algebra of the torus on the Kauffman bracket skein module of the complement of the 3-twist knot. The point is to study the relationship between knot complements and their boundary tori, an idea that has proved very fruitful in knot theory. We place this idea in the context of Chern-Simons theory, where such actions arose in connection with the computation of the noncommutative version of the A-polynomial that was defined by Frohman, the first author, and Lofaro, but they can also be interpreted as quantum mechanical systems. Our goal is to exhibit a detailed example in a part of Chern-Simons theory where examples are scarce.
AB - We determine the action of the Kauffman bracket skein algebra of the torus on the Kauffman bracket skein module of the complement of the 3-twist knot. The point is to study the relationship between knot complements and their boundary tori, an idea that has proved very fruitful in knot theory. We place this idea in the context of Chern-Simons theory, where such actions arose in connection with the computation of the noncommutative version of the A-polynomial that was defined by Frohman, the first author, and Lofaro, but they can also be interpreted as quantum mechanical systems. Our goal is to exhibit a detailed example in a part of Chern-Simons theory where examples are scarce.
KW - 3-twist knot complement
KW - Chern-Simons theory
KW - Kauffman bracket
KW - skein modules
UR - http://www.scopus.com/inward/record.url?scp=85132979976&partnerID=8YFLogxK
U2 - 10.1142/S0218216522500249
DO - 10.1142/S0218216522500249
M3 - Article
AN - SCOPUS:85132979976
SN - 0218-2165
VL - 31
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
IS - 4
M1 - 2250024
ER -