Graphs of Quasicircles and Quasiconformal Homeomorphisms
Geometric Topology
2026-01-16 v1
Abstract
We give a combinatorial characterization of the group of quasiconformal homeomorphisms of a closed, oriented surface of genus at least . In particular, we prove they are exactly the automorphisms of a graph of essential quasicircles on that respect a canonical coarse ordering induced by quality constants. We also discuss the coarse geometry of this graph.
Keywords
Cite
@article{arxiv.2601.09892,
title = {Graphs of Quasicircles and Quasiconformal Homeomorphisms},
author = {Katherine Williams Booth and Alexander Nolte and Yvon Verberne},
journal= {arXiv preprint arXiv:2601.09892},
year = {2026}
}
Comments
22 pages, 5 figures