{"id":"hexagon/2611.00045","pdf":"https://hexagonmath.org/pdf/2611.00045v1","url":"https://hexagonmath.org/abs/2611.00045v1","tags":["math.GT","msc:57R45","msc:58C05"],"score":0,"title":"Torus fibrations on $3$-dimensional manifolds which are smooth functions with finitely many critical values and stable fold maps","domain":"math.GN","source":"hexagon","authors":["Naok Kitazawa"],"reviews":0,"subject":"math.GN","summary":"We present smooth functions which are torus fibrations with finitely many critical values on $3$-dimensional closed manifolds, from (stable) fold maps into the plane. Fold maps are higher dimensional versions of Morse functions and introduced and studied first in the 1950s by Thom and Whitney. Saeki, Sakuma, and so on, are important researchers, studying related singularity theory and differential topology mainly, since the 1990s. $3$-dimensional closed manifolds always admit ones into the plane. Surface fibrations are important tools and objects in complex geometry, symplectic geometry, and…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}