On typical leaves of a measured foliated 2-complex of thin type
Geometric Topology
2015-09-01 v1 Dynamical Systems
Group Theory
Abstract
It is known that all but finitely many leaves of a measured foliated 2-complex of thin type are quasi-isometric to an infinite tree with at most two topological ends. We show that if the foliation is cooriented, and the associated R-tree is self-similar, then a typical leaf has exactly one topological end. We also construct the first example of a foliated 2-complex of thin type whose typical leaf has exactly two topological ends. `Typical' means that the property holds with probability one in a natural sense.
Cite
@article{arxiv.1309.4884,
title = {On typical leaves of a measured foliated 2-complex of thin type},
author = {Ivan Dynnikov and Alexandra Skripchenko},
journal= {arXiv preprint arXiv:1309.4884},
year = {2015}
}
Comments
22 pages, 8 figures