A Thompson group for the basilica

  • James Belk

    Bard College, Annandale-on-Hudson, USA
  • Bradley Forrest

    The Richard Stockton College of New Jersey, Galloway, USA


We describe a Thompson-like group of homeomorphisms of the Basilica Julia set. Each element of this group acts as a piecewise-linear homeomorphism of the unit circle that preserves the invariant lamination for the Basilica. We develop an analogue of tree pair that the group is finitely generated. We also prove that the group is virtually simple.

Cite this article

James Belk, Bradley Forrest, A Thompson group for the basilica. Groups Geom. Dyn. 9 (2015), no. 4, pp. 975–1000

DOI 10.4171/GGD/333