Zhiyun Cheng

activity

20162026

collaborators

13 papers

math.GT2026

A polynomial invariant of planar curves

Zhiyun Cheng, Yin Tian, Tianyu Yuan

We construct a polynomial invariant of planar curves via skein relations, which generalizes Arnold's numerical invariant $St$ .

math.GT2026

GL-racks and coloring invariants of Legendrian knots

Zhiyun Cheng, Zhiyi He

In this paper, we explore the algebraic structure of GL-racks, and demonstrate that finite GL-racks decompose canonically into permutation GL-racks and block GL-racks. As a corolla…

math.GT2024

Coloring invariants for links in $Σ_{g} \times S^{1}$

Zhiyun Cheng, Hongzhu Gao

Let $Σ_{g}$ be a closed oriented surface of genus $g$ , in this paper we discuss how to define coloring invariants and its generalizations for links in $Σ_{g} \times S^{1}$ .

math.GT2023

Intersection graph and writhe polynomial

Zhiyun Cheng

We prove that two virtual knots have equivalent intersection graphs if and only if they have the same writhe polynomial.

math.GT2022

Region crossing change on planar trivalent graphs

Zhiyun Cheng

In this short note, we investigate the effect of region crossing change on planar trivalent graphs.

math.GT2021

Chord index for knots in thickened surfaces

Zhiyun Cheng, Hongzhu Gao, Mengjian Xu

In this note, we construct a chord index homomorphism from a subgroup of $H_{1} (Σ, Z)$ to the group of chord indices of a knot $K$ in $Σ \times I$ . Some knot invariants deriv…

A polynomial invariant of planar curves

GL-racks and coloring invariants of Legendrian knots

Coloring invariants for links in Σg​×S1

Intersection graph and writhe polynomial

Region crossing change on planar trivalent graphs

Chord index for knots in thickened surfaces

Coloring invariants for links in $Σ_{g} \times S^{1}$