8 papers
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 . This is the first such result for genus greater than .
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…
The -character variety of the magic -manifold
Haimiao Chen
We determine the irreducible -character variety of the 3-chain link exterior which is called the `magic -manifold', and deduce a formula for the twisted…
The -character variety of
Haimiao Chen
The knot is the first non-arborescent hyperbolic knot. In 2020, Paoluzzi and Porti found its -character variety with the aid of a computer, but man…
Kauffman bracket skein module of the -pretzel link exterior
Haimiao Chen
We show that the Kauffman bracket skein module of the -pretzel link exterior over is not finitely generated as a module over $\mathbb{Q}(q^…
On the structure of Kauffman bracket skein algebra of a surface
Haimiao Chen
Suppose is a commutative ring with identity and a fixed invertible element such that is invertible. For an oriented surface , let $\mathcal{S}(Σ…
Presentations of Kauffman bracket skein algebras of planar surfaces
Haimiao Chen
Let be a commutative ring with identity and a fixed invertible element , and suppose is invertible in . For each planar surface , we p…
Torsion in Kauffman bracket skein module of a -strand Montesinos knot exterior
Haimiao Chen
For an oriented -manifold , let denote its Kauffman bracket skein module over . We show that admits torsion…