1. Left-orderability of Groups Acting on Bifoliated Planes
- Author
-
Camargo-Rios, Mauro and Lu, Lingfeng
- Subjects
Mathematics - Geometric Topology ,Mathematics - Group Theory - Abstract
We prove that any group acting faithfully on a bifoliated plane while preserving the orientations of both foliations is left-orderable. The proof utilizes a construction of a linear order on the set of ends of the leaf spaces, which takes advantage of the additional structure coming with a bifoliation. Moreover, we build an identification between ends of leaf spaces of the bifoliation and subsets of the boundary circle at infinity, and use it to give a condition for the equivalence between a faithful group action on a bifoliated plane and a faithful group action on the set of ends of the leaf spaces., Comment: 17 pages, 8 figures
- Published
- 2024