论文标题
非孔子类固醇的Orbifold Euler特征
Orbifold Euler characteristics of non-orbifold groupoids
论文作者
论文摘要
对于有限呈现的离散组$γ$，我们引入了Orbifold Euler特征的两个概括，以及$γ$ -Orbifold Euler特征，以适合一类适当的拓扑组素，足以包含所有共同体的适当的li子类固醇。 $γ$ - 欧拉特的特性被定义为相对于closoid轨道空间的欧拉特征的积分，而$γ$ -INERTIA EULER特征是与群体相关的$γ$ -Inertia空间的通常的欧拉特征。一个关键的成分是将O最低结构应用于研究拓扑组素的轨道空间。我们的主要结果是，$γ$ - 欧特尔的特征和$γ$ - 元素特征的特征是重合的，并概括了Gusein-Zade，Luengo和Melle-Hernández的高级Orbifold Euler特征，从压缩的lie组和$γ= \ z}^eell。通过将$γ$ - 欧拉的特征视为拓扑空间的通常欧拉特征，我们证明它在拓扑类固醇类别中是莫里塔不变的，并且满足了古典欧拉特征的熟悉特性。我们在Orbispace图表的有限覆盖范围内，提供了$γ$ - 欧特尔的特征。如果类固醇是通过一组组对翻译群体的ABELIAN扩展，我们将$γ$ - 欧拉的特征与翻译群和组捆绑的特征联系起来。
For a finitely presented discrete group $Γ$, we introduce two generalizations of the orbifold Euler characteristic and $Γ$-orbifold Euler characteristic to a class of proper topological groupoids large enough to include all cocompact proper Lie groupoids. The $Γ$-Euler characteristic is defined as an integral with respect to the Euler characteristic over the orbit space of the groupoid, and the $Γ$-inertia Euler characteristic is the usual Euler characteristic of the $Γ$-inertia space associated to the groupoid. A key ingredient is the application of o-minimal structures to study orbit spaces of topological groupoids. Our main result is that the $Γ$-Euler characteristic and $Γ$-inertia Euler characteristic coincide and generalize the higher-order orbifold Euler characteristics of Gusein-Zade, Luengo, and Melle-Hernández from the case of a translation groupoid by a compact Lie group and $Γ= \mathbb{Z}^\ell$. By realizing the $Γ$-Euler characteristic as the usual Euler characteristic of a topological space, we demonstrate that it is Morita invariant in the category of topological groupoids and satisfies familiar properties of the classical Euler characteristic. We give an additional formulation of the $Γ$-Euler characteristic for a cocompact proper Lie groupoid in terms of a finite covering by orbispace charts. In the case that the groupoid is an abelian extension of a translation groupoid by a bundle of groups, we relate the $Γ$-Euler characteristics to those of the translation groupoid and bundle of groups.
