Circle packings, kissing reflection groups and critically fixed anti-rational maps
Dynamical Systems
2022-02-07 v2 Group Theory
Geometric Topology
Abstract
In this paper, we establish an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps. The correspondence, which is expressed using simple planar graphs, has several dynamical consequences. As an application of this correspondence, we give complete answers to geometric mating problems for critically fixed anti-rational maps.
Keywords
Cite
@article{arxiv.2007.03558,
title = {Circle packings, kissing reflection groups and critically fixed anti-rational maps},
author = {Russell Lodge and Yusheng Luo and Sabyasachi Mukherjee},
journal= {arXiv preprint arXiv:2007.03558},
year = {2022}
}
Comments
49 pages, 14 figures. The last two sections of v1 are moved to the sequel of this paper. Final version, to appear in Forum of Math. Sigma