A Thompson Group for the Basilica

Details A Thompson Group for the Basilica A Thompson Group for the Basilica

2012-01-20

arxiv.org/abs/1201.4225v1

Mathematics

Group Theory

23 pages, 31 figures

Scientific paper

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 diagrams for this group which we call arc pair diagrams, and we use these diagrams to prove that the group is finitely generated. We also prove that the group is virtually simple.

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