arXiv subjects

Gao Hongzhu

Publications and source records attributed to Gao Hongzhu.

3 recordsLinked to original sources

arXiv2021

The rational cohomology groups of the classifying spaces of Kac-Moody groups

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 to infinite". That is, for a Kac-Moody group G(A) of infinite type, the input data for computation are the rational cohomology of classifying spaces of parabolic subgroups of G(A)(which are of finite type), and the homomorphisms induced by inclusions of these subgroups. In some special cases, we can further determine the cohomology rings. Our method also applies to study the mod p cohomology of the classifying spaces of Kac-Moody groups.

math.AT↗

arXiv2016

Differential geometry of general affine plane curves

In this paper we study the general affine geometry of curves in affine space $A^2$. For a regular plane curves we define two kinds of moving frames. The first is of minimal order in all moving frames.The second is the Frenet moving frame. We get the moving equations of these moving frames. And we prove that curvature and signature are the complete invariants of regular curves. As application we give a complete classification of constant curvature curves in $A^2$.

math.DG↗

arXiv2015

A Geometric Definition Of Schubert Polynomials and Dual Schubert Polynomials For Classical Lie Groups

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 embedding the flag manifold of a classical Lie group into its corresponding infinite dimensional projective Stiefel manifold(which is homotopic to the product of infinite dimensional complex projective space $\mathbb{C}P^{\infty}$), we define the Schubert polynomials and dual Schubert polynomials. Finally we discuss the property and the computation of these polynomials.

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