On the Group of Homeomorphisms of the Basilica - Neretin, Yury (Topology Proceedings, 2024)
We show that the group of all homeomorphisms of the Basilica fractal coincides with a group of transformations of a certain non-locally finite ribbon tree (a ribbon graph is a graph with a fixed cyclic order of edges at each vertex). Also, we show that the Basilica Thompson group defined by James Belk and Bradley Forrest is dense in the group of all orientation preserving homeomorphisms of the Basilica.