Communications in Analysis and Geometry

Volume 31 (2023)

Number 6

Stable maps and hyperbolic links

Pages: 1405 – 1432

DOI: https://dx.doi.org/10.4310/CAG.2023.v31.n6.a3

Authors

Ryoga Furutani (Department of Mathematics and International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, Higashi-Hiroshima, Japan)

Yuya Koda (Department of Mathematics, Hiyoshi Campus, Keio University, Kohoku, Yokohama, Japan; and International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, Higashi-Hiroshima, Japan)

Abstract

A stable map of a closed orientable $3$-manifold into the real plane is called a stable map of a link in the manifold if the link is contained in the set of definite fold points. We give a complete characterization of the hyperbolic links in the $3$-sphere that admit stable maps into the real plane with exactly one (connected component of a) fiber having two singular points.

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Received 4 March 2021

Accepted 25 May 2021

Published 9 August 2024