arXiv subjects

Gakuto Kato

Publications and source records attributed to Gakuto Kato.

3 recordsLinked to original sources

arXiv2026

Links and singularities of stable maps from $3$-manifolds to surfaces

For any two links in the $3$-sphere, we provide a visual construction of a stable map $f$ from the $3$-sphere to the Euclidean plane such that $f$ has no cusp points, the set of definite (resp. indefinite) fold points of $f$ is isotopic to the first (resp. second) given link, and $f$ does not have a certain type of singular fibers. Moreover, we obtain a similar result for any $3$-manifold by setting the target space to the $2$-sphere.

math.GT↗

arXiv2025

On a construction of stable maps from 3-manifolds into surfaces

For any link in the $3$-sphere, we give a visual construction of a stable map $f$ from the $3$-sphere into the real plane enjoying the following properties; $f$ has no cusp point, the set of definite fold points of $f$ is isotopic to the given link and $f$ only has certain type of fibers containing two indefinite fold points. As a corollary, we obtain a similar stable map from every closed orientable $3$-manifold into the $2$-sphere.

math.GT↗

arXiv2025

Two-bridge links and stable maps into the plane

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.

math.GT↗