Hierarchy of graph matchbox manifolds
Abstract
We study a class of graph foliated spaces, or graph matchbox manifolds, initially constructed by Kenyon and Ghys. For graph foliated spaces we introduce a quantifier of dynamical complexity which we call its level. We develop the fusion construction, which allows us to associate to every two graph foliated spaces a third one which contains the former two in its closure. Although the underlying idea of the fusion is simple, it gives us a powerful tool to study graph foliated spaces. Using fusion, we prove that there is a hierarchy of graph foliated spaces at infinite levels. We also construct examples of graph foliated spaces with various dynamical and geometric properties.
Keywords
Cite
@article{arxiv.1107.5303,
title = {Hierarchy of graph matchbox manifolds},
author = {Olga Lukina},
journal= {arXiv preprint arXiv:1107.5303},
year = {2012}
}
Comments
New examples added at the end of Section 2; Introduction is rewritten. To appear in Topology and its Applications