单形和3维立方体乘积上小覆盖的等变协边类的个数

本文研究了小覆盖的等变协边分类. 利用示性函数和Stong同态确定了单形和3维立方体乘积上小覆盖的等变协边类的个数, 推广了现有文献中的相关结果.     

棱柱上的小覆盖的等变配边分类

多面体上的小覆盖的等变配边类是由它的切表示集所决定的.本文通过将棱柱上的小覆盖的切表示集约化到一种素形式,来确定其等变配边分类.     

L?bell多面体上的小覆盖

计算了L?bell多面体上的小覆盖的等变微分同胚类的个数.在1991年,Davis和Januszkiewicz提出了小覆盖的概念,给出了组合和拓扑间的一种直接联系,并证明了单凸多面体上的特征映射(Z~n_2染色)与该多面体上的小覆盖一一对应.文中作者给出了L?bell多面体上的自同构群和染色规律,结合Burnside引理计算了一般的L?bell多面体上的小覆盖的等变微分同胚类的个数.     

L\"obell多面体上的小覆盖

计算了L\"{o}bell多面体上的小覆盖的等变微分同胚类的个数. 在1991年, Davis和Januszkiewicz提出了小覆盖的概念, 给出了组合和拓扑间的一种直接联系, 并证明了单凸多面体上的特征映射($\mathbb{Z}_2^n$染色)与该多面体上的小覆盖一一对应. 文中作者给出了L\"{o}bell多面体上的自同构群和染色规律, 结合Burnside引理计算了一般的L\"{o}bell多面体上的小覆盖的等变微分同胚类的个数.     

棱柱和多边形上可定向的小覆盖

计算了棱柱和多边形上可定向小覆盖的等变同胚类的个数.     

流形 RP(2k+1)上的光滑对合

本文证明了2k+1维实射影空间 RP(2k+1)上的光滑对合在等变协边意义下仅有 j+1种,它们是1,τ_0,τ_2,…,τ_(2i),其中 i 为满足2i≤k 的最大整数.     

带有对合的流形的协边类Ⅱ

本文考虑如下问题:对于给定的 n 维协边类 α,n-1维协边类β_(n-1)和 n-k_i维协边类β_(n-k_i)(1相似文献   

扩展的Bianchi恒等式及其在几何流演化方程中的应用

在初始版本的第一,二Bianchi恒等式的基础上,利用二阶或三阶协变导数引申出扩展的二阶协变和三阶协变Bianchi恒等式.这类二阶协变Bianchi恒等式在黎曼曲率张量沿着两类特殊的几何流-里奇(Ricci)流和双曲几何流的演化方程中有一定的应用.给出这方面的应用例子并加以阐述.     

变结构面板协整检验的响应面函数研究

Panel-ρ检验是常用的异质面板数据协整检验统方法,本文通过Monte Carlo模拟分析Panel-ρ协整检验方法的小样本性质,以及该方法对于变结构面板协整检验的检验功效.结果表明,在小样本情况下Panel-ρ统计量在原假设下的渐进分布会不同于该统计量的理论渐进分布,而且面板数据中存在的结构变化也会对渐进分布产生影响,从而降低Panel-ρ检验的检验功效.为了得到更加符合实际样本情况的统计量临界值,通过Monte Carlo模拟方法得到Panel-ρ协整检验方法的响应面函数,建立了统计量的临界值与面板数据的样本容量、结构变化类型的直接函数关系.Monte Carlo模拟检验表明,响应面函数法确实能够改善Panel-ρ协整检验的检验功效,在小样本容量和具有结构变化的情况下保证了面板协整检验的有效性.     

等变上同调与ech超上同调的同构定理

首先证明了任意一个等变微分流形都存在等变良好开覆盖,且等变良好开覆盖集所组成的集合在全部开覆盖组成的集合中共尾.在此基础上,证明了等变上同调与ech超上同调的同构.此定理可应用于实代数簇的Deligne上同调研究.     

Equivariant cobordism of flag varieties and of symmetric varieties

We obtain an explicit presentation for the equivariant cobordism ring of a complete flag variety. An immediate corollary is a Borel presentation for the ordinary cobordism ring. Another application is an equivariant Schubert calculus in cobordism. We also describe the rational equivariant cobordism rings of wonderful symmetric varieties of minimal rank.     

Equivariant pretheories and invariants of torsors

In the present paper we introduce and study the notion of an equivariant pretheory (basic examples are equivariant Chow groups of Edidin and Graham, Thomason??s equivariant K-theory and equivariant algebraic cobordism). Using the language of equivariant pretheories we generalize the theorem of Karpenko and Merkurjev on G-torsors and rational cycles. As an application, to every G-torsor E and a G-equivariant pretheory we associate a ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information about the motivic J-invariant of E, in the case of Grothendieck??s K ₀ indexes of the respective Tits algebras and in the case of algebraic cobordism ?? it gives a quotient of the cobordism ring of G.     

CLASSIFYING INVOLUTIONS ON PR( 2k) UP TO EQUIVARIANT COBORDISM

It is proved that there are exactly k + 1 involutions on RP(2k) up to equivariant cobordism.     

Algebraic cobordism revisited

We define a cobordism theory in algebraic geometry based on normal crossing degenerations with double point singularities. The main result is the equivalence of double point cobordism to the theory of algebraic cobordism previously defined by Levine and Morel. Double point cobordism provides a simple, geometric presentation of algebraic cobordism theory. As a corollary, the Lazard ring given by products of projective spaces rationally generates all nonsingular projective varieties modulo double point degenerations. Double point degenerations arise naturally in relative Donaldson–Thomas theory. We use double point cobordism to prove all the degree 0 conjectures in Donaldson–Thomas theory: absolute, relative, and equivariant.     

Small covers over prisms

In this paper we calculate the number of equivariant diffeomorphism classes of small covers over a prism.     

Operations on 3-Dimensional Small Covers

The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura＇s theorem on the construction of oriented 3-dimensional small covers and the Lu-Yu＇s theorem on the construction of all 3-dimensional small covers are improved. Moreover, for a construction of 3-dimensional 2-torus manifolds, it is shown that all operations can be obtained by using the equivariant surgeries.     

Orbit configuration spaces of small covers and quasi-toric manifolds

In this article,we investigate the orbit configuration spaces of some equivariant closed manifolds over simple convex polytopes in toric topology,such as small covers,quasi-toric manifolds and(real)moment-angle manifolds;especially for the cases of small covers and quasi-toric manifolds.These kinds of orbit configuration spaces have non-free group actions,and they are all noncompact,but still built via simple convex polytopes.We obtain an explicit formula of the Euler characteristic for orbit configuration spaces of small covers and quasi-toric manifolds in terms of the h-vector of a simple convex polytope.As a by-product of our method,we also obtain a formula of the Euler characteristic for the classical configuration space,which generalizes the Félix-Thomas formula.In addition,we also study the homotopy type of such orbit configuration spaces.In particular,we determine an equivariant strong deformation retraction of the orbit configuration space of 2 distinct orbit-points in a small cover or a quasi-toric manifold,which allows to further study the algebraic topology of such an orbit configuration space by using the Mayer-Vietoris spectral sequence.