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. 975–1000DOI 10.4171/GGD/333