25 citations · 36 across the 11 of their papers we have counts for
7 papers · 1 filter
Coloring invariants for links in
Zhiyun Cheng, Hongzhu Gao
Let be a closed oriented surface of genus , in this paper we discuss how to define coloring invariants and its generalizations for links in .
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 to the group of chord indices of a knot in . Some knot invariants deriv…
Some remarks on the chord index
Zhiyun Cheng, Hongzhu Gao, Mengjian Xu
In this paper we discuss how to define a chord index via smoothing a real crossing point of a virtual knot diagram. Several polynomial invariants of virtual knots and links can be…
Integral positive (negative) quandle cocycle invariants are trivial for knots
Zhiyun Cheng, Hongzhu Gao
In this note we prove that for any finite quandle and any 2-cocycle $ϕ\in Z^2_{Q\pm}(X; \mathds{Z})$, the cocycle invariant is trivial for all knots .
Positive quandle homology and its applications in knot theory
Zhiyun Cheng, Hongzhu Gao
Algebraic homology and cohomology theories for quandles have been studied extensively in recent years. With a given quandle 2(3)-cocycle one can define a state-sum invariant for kn…
A polynomial invariant of virtual links
Zhiyun Cheng, Hongzhu Gao
In this paper, we define some polynomial invariants for virtual knots and links. In the first part we use Manturov's parity axioms to obtain a new polynomial invariant of virtual k…
On region crossing change and incidence matrix
Zhiyun Cheng, Hongzhu Gao
In a recent work of Ayaka Shimizu, she defined an operation named region crossing change on link diagrams, and showed that region crossing change is an unknotting operation…