New perspectives on Grigorchuk-Machì Group (Neelam, University of Utah)

21.04.2026 10:30

Grigorchuk and Machì introduced a group Γ of intermediate growth that is a subgroup of Aut(R). They do this by showing that the group is left-orderable. In 2008, Andres Navas gave an explicit description of a group G of homeomorphisms of [0,1]. In his paper, he mentions that G is isomorphic to the geometric realization of Γ. In this talk, we prove this claim by showing that Γ is isomorphic to G. In addition, we see that these groups are isomorphic to the braided Grigorchuk group defined by Skipper and Zaremsky in 2023 which has recently appeared in the study of big mapping class groups. More broadly, this construction of braiding Grigorchuk group fits into a program relating self-similar groups to their braided analogs. As an example of this, I will discuss a general theorem where the amenability property gets preserved under braiding.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 21.04.2026, Séminaire "Groupes et géométrie"

entrée libre