Haimiao Chen

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20232026

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8 papers · 1 filter

math.GT2026

Presentations of skein algebras of genus 2

Haimiao Chen

We give a presentation for the Kauffman bracket skein algebra of a closed or one-holed oriented surface of genus $2$ . This is the first such result for genus greater than $1$ .

math.GT2026

Computing Alexander polynomials for arborescent links

Haimiao Chen

Alexander polynomial was born one century ago, but explicit formulas have been found for only a few families of links. In this paper, we present an efficient method of computing Al…

math.GT2026

The $SL (2, C)$ -character variety of the magic $3$ -manifold

Haimiao Chen

We determine the irreducible $SL (2, C)$ -character variety of the 3-chain link exterior which is called the `magic $3$ -manifold', and deduce a formula for the twisted…

math.GT2025

The $SL (2, C)$ -character variety of $8_{18}$

Haimiao Chen

The knot $8_{18}$ is the first non-arborescent hyperbolic knot. In 2020, Paoluzzi and Porti found its $SL (2, C)$ -character variety with the aid of a computer, but man…

math.GT2025

Kauffman bracket skein module of the $(3, 3, 3, 3)$ -pretzel link exterior

Haimiao Chen

We show that the Kauffman bracket skein module of the $(3, 3, 3, 3)$ -pretzel link exterior over $Q (q^{\frac{1}{2}})$ is not finitely generated as a module over $\mathbb{Q}(q^…

math.GT2024

On the structure of Kauffman bracket skein algebra of a surface

Haimiao Chen

Suppose $R$ is a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$ such that $q + q^{- 1}$ is invertible. For an oriented surface $Σ$ , let $\mathcal{S}(Σ…

math.GT2023

Presentations of Kauffman bracket skein algebras of planar surfaces

Haimiao Chen

Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$ , and suppose $q + q^{- 1}$ is invertible in $R$ . For each planar surface $Σ_{0, n + 1}$ , we p…

math.GT2023

Torsion in Kauffman bracket skein module of a $4$ -strand Montesinos knot exterior

Haimiao Chen

For an oriented $3$ -manifold $M$ , let $S (M)$ denote its Kauffman bracket skein module over $Z [q^{\pm \frac{1}{2}}]$ . We show that $S (M)$ admits torsion…

Presentations of skein algebras of genus 2

Computing Alexander polynomials for arborescent links

The SL(2,C)-character variety of the magic 3-manifold

The SL(2,C)-character variety of 818​

Kauffman bracket skein module of the (3,3,3,3)-pretzel link exterior

On the structure of Kauffman bracket skein algebra of a surface

Presentations of Kauffman bracket skein algebras of planar surfaces

Torsion in Kauffman bracket skein module of a 4-strand Montesinos knot exterior

The $SL (2, C)$ -character variety of the magic $3$ -manifold

The $SL (2, C)$ -character variety of $8_{18}$

Kauffman bracket skein module of the $(3, 3, 3, 3)$ -pretzel link exterior

Torsion in Kauffman bracket skein module of a $4$ -strand Montesinos knot exterior