Two-bridge links and stable maps into the plane

Abstract

We give a visual construction of stable maps from the $3$-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.

14 pages, 17 figures. v2. Theorem 1.1 has been improved. A corollary on stable map complexity has been added