Knots and Their Related -Series

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Authors: Garoufalidis, Stavros, Zagier, Don
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212049
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Knots and Their Related -Series. Stavros Garoufalidis and Don Zagier. SIGMA 19 (2023), 082, 39 pages

We discuss a matrix of periodic holomorphic functions in the upper and lower half-plane, which can be obtained from a factorization of an Andersen-Kashaev state integral of a knot complement with remarkable analytic and asymptotic properties that define a PSL₂(ℤ)-cocycle on the space of matrix-value...