Groups, Geometry, and Dynamics

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Volume 9, Issue 4, 2015, pp. 975–1000
DOI: 10.4171/GGD/333

Published online: 2015-11-16

A Thompson group for the basilica

James Belk[1] and Bradley Forrest[2]

(1) Bard College, Annandale-on-Hudson, USA
(2) 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.

Keywords: Tompson’s groups, piecewise-linear homeomorphism, Julia set, invariant lamination

Belk James, Forrest Bradley: A Thompson group for the basilica. Groups Geom. Dyn. 9 (2015), 975-1000. doi: 10.4171/GGD/333