# The groupoid C*-algebra of a rational map

### Klaus Thomsen

Aarhus University, Denmark

## 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.

## Cite this article

Klaus Thomsen, The groupoid C*-algebra of a rational map. J. Noncommut. Geom. 8 (2014), no. 1, pp. 217–264

DOI 10.4171/JNCG/154