A weak homotopy equivalence type result related to Kirchberg algebras

摘要

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-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.