Representations of the Kauffman bracket skein algebra of the punctured torus

2014 ◽  
Vol 225 (1) ◽  
pp. 45-55 ◽  
Author(s):  
Jea-Pil Cho ◽  
Răzvan Gelca
2017 ◽  
Vol 26 (12) ◽  
pp. 1750081
Author(s):  
Sang Youl Lee

In this paper, we introduce a notion of virtual marked graphs and their equivalence and then define polynomial invariants for virtual marked graphs using invariants for virtual links. We also formulate a way how to define the ideal coset invariants for virtual surface-links using the polynomial invariants for virtual marked graphs. Examining this theory with the Kauffman bracket polynomial, we establish a natural extension of the Kauffman bracket polynomial to virtual marked graphs and found the ideal coset invariant for virtual surface-links using the extended Kauffman bracket polynomial.


2018 ◽  
Vol 215 (2) ◽  
pp. 609-650 ◽  
Author(s):  
Charles Frohman ◽  
Joanna Kania-Bartoszynska ◽  
Thang Lê
Keyword(s):  

2015 ◽  
Vol 22 (2) ◽  
pp. 485-499 ◽  
Author(s):  
Hengnan Hu ◽  
Ser Peow Tan ◽  
Ying Zhang
Keyword(s):  

2019 ◽  
Vol 28 (14) ◽  
pp. 1950083 ◽  
Author(s):  
Takeyoshi Kogiso ◽  
Michihisa Wakui

In this paper, we build a bridge between Conway–Coxeter friezes (CCFs) and rational tangles through the Kauffman bracket polynomials. One can compute a Kauffman bracket polynomial attached to rational links by using CCFs. As an application, one can give a complete invariant on CCFs of zigzag-type.


2010 ◽  
Vol 19 (08) ◽  
pp. 1001-1023 ◽  
Author(s):  
XIAN'AN JIN ◽  
FUJI ZHANG

It is well known that Jones polynomial (hence, Kauffman bracket polynomial) of links is, in general, hard to compute. By now, Jones polynomials or Kauffman bracket polynomials of many link families have been computed, see [4, 7–11]. In recent years, the computer algebra (Maple) techniques were used to calculate link polynomials for various link families, see [7, 12–14]. In this paper, we try to design a maple program to calculate the explicit expression of the Kauffman bracket polynomial of Montesinos links. We first introduce a family of "ring of tangles" links, which includes Montesinos links as a special subfamily. Then, we provide a closed-form formula of Kauffman bracket polynomial for a "ring of tangles" link in terms of Kauffman bracket polynomials of the numerators and denominators of the tangles building the link. Finally, using this formula and known results on rational links, the Maple program is designed.


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