一般Orbifold和圈积的广义Orbifold欧拉示性数
Generalized orbifold Euler characteristics for general orbifolds and wreath products
摘要：
我们引入了由Orbifold广群$\mathcal{G}$表示的一般Orbifold $Q$的$Γ$-Euler-Satake特征，将Bryan-Fulman和Tamanoi的广义Orbifold欧拉示性数推广到不一定是全局同形的Orbifold.这些欧拉示性数中的每一个被定义为轨道的$Γ$ -扇区的空间的欧拉-佐竹示性，其中$Γ$是一个离散群。我们研究了这些特性的行为下的产品操作适用于组$Γ$以及orbifold和现有的欧拉示性数的orbifold建立他们的关系。作为应用，我们将Tamanoi，Wang和Zhou关于整体商轨道折叠的圈对称积的欧拉示性数和Hodge数的公式推广到紧连通李群几乎自由作用的圈对称积的情形.
英文摘要：
We introduce the $Γ$-Euler-Satake characteristics of a general orbifold $Q$ presented by an orbifold groupoid $\mathcal{G}$, generalizing to orbifolds that are not necessarily global quotients the generalized orbifold Euler characteristics of Bryan-Fulman and Tamanoi. Each of these Euler characteristics is defined as the Euler-Satake characteristic of the space of $Γ$-sectors of the orbifold where $Γ$ is a finitely generated discrete group. We study the behavior of these characteristics under product operations applied to the group $Γ$ as well as the orbifold and establish their relationships to existing Euler characteristics for orbifolds. As applications, we generalize formulas of Tamanoi, Wang, and Zhou for the Euler characteristics and Hodge numbers of wreath symmetric products of global quotient orbifolds to the case of quotients by compact, connected Lie groups acting almost freely.
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