A weak homotopy equivalence type result related to Kirchberg algebras

  • Masaki Izumi

    Kyoto University, Japan
  • Hiroki Matui

    Chiba University, Japan
A weak homotopy equivalence type result related to Kirchberg algebras cover

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Abstract

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- group actions on Kirchberg algebras. As a special case, we show that the -groups of the continuous asymptotic centralizer are isomorphic to the -groups of the Kirchberg algebra.

Cite this article

Masaki Izumi, Hiroki Matui, A weak homotopy equivalence type result related to Kirchberg algebras. J. Noncommut. Geom. 14 (2020), no. 4, pp. 1325–1363

DOI 10.4171/JNCG/392