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

Gakuto Kato

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arXiv · 2508.21337

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

Gakuto Kato

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Abstract

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.

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Gakuto Kato. 2025-08-29. On a construction of stable maps from 3-manifolds into surfaces. https://arxiv.org/abs/2508.21337

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