The groupoid C*-algebra of a rational map

2012/02/13 by Thomsen, Klaus
#37F10 #46L35 #58B34 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1202.2659

Abstract

This paper contains a quite detailed description of the C*-algebra arising from the transformation groupoid of a rational map of degree at least two on the Riemann sphere. The algebra is decomposed stepwise via extensions of familiar C*-algebras whose nature depend on the structure of the Julia set and the stable regions in the Fatou set, as well as on the behaviour of the critical points.

Related

• The K-theory of the C*-algebras associated to rational functions
• C*-algebras associated with branched coverings
• Decomposing the C*-algebras of groupoid extensions
• C*-algebras of groupoid morphisms
• Invariant graphs in Julia sets and decompositions of rational maps