We obtain a weak homotopy equivalence type result between two topological groups associated with a Kirchberg algebra: the unitary group of the continuous asymptotic centralizer and the loop group of the automorphism group of the stabilization. This result plays a crucial role in our subsequent work on the classification of poly-$\mathbb Z$ group actions on Kirchberg algebras. As a special case, we show that the $K$-groups of the continuous asymptotic centralizer are isomorphic to the $KK$-groups of the Kirchberg algebra.

中文翻译：

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与Kirchberg代数有关的弱同伦等价类型结果

我们获得了两个与Kirchberg代数关联的拓扑组之间的弱同伦等价类型结果：连续渐近扶正器的ary组和稳定化自同构组的环组。这个结果在我们随后的关于Kirchberg代数上的poly $ \ mathbb Z $群作用的分类的工作中起着至关重要的作用。作为一个特例，我们证明连续渐近扶正器的$ K $-基团与Kirchberg代数的$ KK $-基团同构。