# Journal of Operator Theory

Volume 75, Issue 1, Winter 2016  pp. 163-193.

Independent resolutions for totally disconnected dynamical systems. II. $C^*$-algebraic case

Authors:  Xin Li (1) and Magnus D. Norling (2)
Author institution: (1) School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, U.K.
(2) Institute of Mathematics, University of Oslo, P.b. 1053 Blindern, 0316 Oslo, Norway

Summary: We develop the notion of independent resolutions for crossed products attached to totally disconnected dynamical systems. If such a crossed product admits an independent resolution of finite length, then its K-theory can be computed (at least in principle) by analysing the corresponding six-term exact sequences. Building on our previous paper on algebraic independent resolutions, we give a criterion for the existence of finite length independent resolutions. Moreover, we illustrate our ideas in various concrete examples.

DOI: http://dx.doi.org/10.7900/jot.2014dec22.2061
Keywords: $C^*$-algebras, K-theory