论文标题
（CO）同源性和其他TSI组不变的分类的动态障碍
Dynamical obstructions to classification by (co)homology and other TSI-group invariants
论文作者
论文摘要
本着赫乔斯（Hjorth）的湍流理论的精神，我们引入了“不平衡性”：通过波兰人群体的行动对轨道对等关系进行分类的新动态阻碍，而波兰群体接受了两侧不变的度量（TSI）。由于阿贝尔群体是TSI，因此不平衡可用于识别无法通过经典同源性和协同学理论解决哪些分类问题。 在应用方面，我们表明，连续跟踪$ c^*$ - 代数以及Hermitian系列捆绑包的同构的等效性不受TSI组的行动分类。在此过程中，我们表明，$ s _ {\ infty} $的任何两个非紧凑子组的花环产物承认其轨道等效关系通常对TSI组的任何动作都具有良好性，并且我们推断出一个不可分类的轨道等效性相关性，该轨道等效性关系是由TSI组分类的。
In the spirit of Hjorth's turbulence theory, we introduce "unbalancedness": a new dynamical obstruction to classifying orbit equivalence relations by actions of Polish groups which admit a two side invariant metric (TSI). Since abelian groups are TSI, unbalancedness can be used for identifying which classification problems cannot be solved by classical homology and cohomology theories. In terms of applications, we show that Morita equivalence of continuous-trace $C^*$-algebras, as well as isomorphism of Hermitian line bundles, are not classifiable by actions of TSI groups. In the process, we show that the Wreath product of any two non-compact subgroups of $S_{\infty}$ admits an action whose orbit equivalence relation is generically ergodic against any action of a TSI group and we deduce that there is an orbit equivalence relation of a CLI group which is not classifiable by actions of TSI groups.
