25 citations · 36 across the 11 of their papers we have counts for
11 papers
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 .
The rational cohomology groups of the classifying spaces of Kac-Moody groups
Zhao Xu-an, Gao Hongzhu, Ruan Yangyang
In this paper, we compute the rational cohomology groups of the classifying space of a simply connected Kac-Moody group of infinite type. The fundamental principle is "from finite…
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…
The rational cohomology Hopf algebra of a generic Kac-Moody group
Xu-an Zhao, Hongzhu Gao
In this paper we determine the rational homotopy type of the classifying space of a generic Kac-Moody group by computing its rational cohomology ring. As an application we determin…
General affine differential geometry of surfaces in affine space , I: the elliptical case
Xu-an Zhao, Hongzhu Gao
In this paper we study the general affine differential geometry of surfaces in affine space . For a regular elliptical surface we define a moving frame of minimal order and ge…
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…
A Geometric Definition Of Schubert Polynomials and Dual Schubert Polynomials For Classical Lie Groups
Zhao Xu-an, Gao Hongzhu
In this paper, we first discuss the topological properties of projective Stiefel manifolds, we compute their cohomology rings and classify their cohomology endomorphisms; Then by e…
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…