Two-bridge links and stable maps into the plane
Geometric Topology
2025-01-15 v3
Abstract
We give a visual construction of stable maps from the -sphere into the real plane enjoying the following properties; the set of definite fold points coincides with a given two-bridge link and the map only admits certain types of fibers containing two indefinite fold points. As a corollary, we determine the stable map complexities defined by Koda and Ishikawa for some two-bridge link exteriors.
Cite
@article{arxiv.2405.14296,
title = {Two-bridge links and stable maps into the plane},
author = {Kazuhiro Ichihara and Gakuto Kato},
journal= {arXiv preprint arXiv:2405.14296},
year = {2025}
}
Comments
14 pages, 17 figures. v2. Theorem 1.1 has been improved. A corollary on stable map complexity has been added