arXiv subjects

Shun Sawabe

Publications and source records attributed to Shun Sawabe.

3 recordsLinked to original sources

arXiv2024

On the Annihilating polynomial of the Colored Jones Polynomial for Some Links

In this paper, we consider polynomials and ideals obtained from the colored Jones polynomial in both commutative and noncommutative cases. In the commutative case, this ideal contains polynomials that can be regarded as the link version of the $A$-polynomial; in the noncommutative case, it consists of annihilating polynomials of the colored Jones polynomial and can be regarded as the link version of the $A_q$-polynomial. Moreover, we formulate the link version of the AJ conjecture.

math.GT↗

arXiv2023

On the Potential Function of the Colored Jones Polynomial with Arbitrary Colors

We consider the potential function of the colored Jones polynomial for a link with arbitrary colors and obtain the cone-manifold structure for the link complement. In addition, we establish a relationship between a saddle point equation and hyperbolicity of the link complement. This provides evidence for the Chen-Yang conjecture on the link complement.

math.GT↗

arXiv2022

On the Potential Function of the Colored Jones Polynomial and the AJ conjecture

The $A$-polynomial is conjectured to be obtained from the potential function of the colored Jones polynomial by elimination. The AJ conjecture also implies the relationship between the $A$-polynomial and the colored Jones polynomial. In this paper, we connect these conjectures from the perspective of the parametrized potential function.

math.GT↗