Hongzhu Gao

activity

20182024

collaborators

6 papers

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.AT2021

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…

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…

math.GT2018

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…

math.AT2018

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…

math.DG2018

General affine differential geometry of surfaces in affine space $A^{3}$ , I: the elliptical case