Work

The planar 3-colorable subgroup ε of Thompson’s group F and its even part

Year: 2024

Type: article

Abstract: We study the planar 3-colorablesubgroup $\mathcal{E}$ of Thompson’s group F and its even part ${\mathcal{E}_{\rm EVEN}}$ . The latter is obtained by cutting $\mathcal{E}$ with a finite index subgroup of F isomorphic to F, namely the rectangular subgroup $K_{(2,2)}$ . We show that the even part ${\mathcal{E}_{\rm EVEN}}$ of the planar 3-colorable subgroup admits a description in terms of stabilisers of suitable subsets of dyadic rationals. As a consequence ${\mathcal{E}_{\rm EVEN}}$ is closed in the sense of Golan and Sapir. We then study three quasi-regular representations associated with ${\mathcal{E}_{\rm EVEN}}$ : two are shown to be irreducible and one to be reducible.

Source: Proceedings of the Edinburgh Mathematical Society

DOI: 10.1017/s0013091524000452

Authors: Valeriano Aiello, Tatiana Nagnibeda

Institutions: Sapienza University of Rome, University of Geneva

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, University of Bern

Award: G5599649393