Ziggurat fringes are self-similar
Geometric Topology
2016-01-06 v1 Dynamical Systems
Group Theory
Abstract
We give explicit formulae for fringe lengths of the Calegari-Walker Ziggurats -- i.e. graphs of extremal rotation numbers associated to positive words in free groups. These formulae reveal (partial) integral projective self-similarity in ziggurat fringes, which are low-dimensional projections of characteristic polyhedra on the bounded cohomology of free groups. This explains phenomena observed experimentally by Gordenko and Calegari-Walker.
Cite
@article{arxiv.1503.04227,
title = {Ziggurat fringes are self-similar},
author = {Subhadip Chowdhury},
journal= {arXiv preprint arXiv:1503.04227},
year = {2016}
}
Comments
20 pages, 8 figures