Journal of Noncommutative Geometry

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Volume 8, Issue 1, 2014, pp. 217–264
DOI: 10.4171/JNCG/154

Published online: 2014-03-20

The groupoid C*-algebra of a rational map

Klaus Thomsen[1]

(1) Aarhus University, Denmark

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.

Keywords: C*-algebra, groupoid, holomorphic dynamics, rational map

Thomsen Klaus: The groupoid C*-algebra of a rational map. J. Noncommut. Geom. 8 (2014), 217-264. doi: 10.4171/JNCG/154