arXiv subjects

Koki Iwakura

Publications and source records attributed to Koki Iwakura.

4 recordsLinked to original sources

arXiv2026

On submersions with definite folds of manifolds with boundary into Euclidean spaces

Submersions with definite folds are submersions on manifolds with boundary whose restrictions to the boundary are definite fold maps. In this paper, we study differential-topological properties of manifolds with boundary admitting such maps into Euclidean spaces. When the target is $\mathbb{R}$, we obtain restrictions on the diffeomorphism types of the source manifolds by using results for m-functions. For targets of dimension greater than one, we focus on the cases where the restrictions to the boundary are round fold maps or image simple fold maps, both defined by conditions on the singular value set. Then, we study the diffeomorphism types and Euler characteristics of manifolds admitting such maps. These results have applications to non-singular extensions of definite fold maps.

math.GT↗

arXiv2025

Topology of boundary special generic maps into Euclidean spaces

We introduce boundary special generic maps, a class of submersions from manifolds with boundary to Euclidean spaces whose restriction to the boundary has only boundary definite fold points as its singular points. We derive the differential-topological restrictions imposed by the existence of such maps on the global structure of the source manifolds. Furthermore, we apply our results to the non-singular extension problem, which asks when a map on a closed manifold extends to a non-singular map on a manifold with boundary, and obtain new results on non-singular extensions of special generic maps.

math.GT↗

arXiv2024

Non-singular extensions of horizontal stable fold maps from surfaces to the plane

In this paper, we study the non-singular extension problem of horizontal stable fold maps. This problem asks what conditions ensure the existence of a submersion whose restriction to the boundary coincides with a given map, called a non-singular extension. By defining a combinatorial object called a pairing map, we prove that the existence of a non-singular extension is equivalent to the existence of a pairing map. Furthermore, to facilitate the application of the main theorem, we compute the Euler characteristics and the fundamental groups of compact $3$-dimensional manifolds that serve as the source manifolds of non-singular extensions.

math.GT↗

arXiv2023

Non-singular extensions of circle-valued Morse functions

In this paper, we consider the non-singular extension problem for circle-valued Morse functions on closed orientable surfaces. The problem asks, given a circle-valued Morse function $f\colon M\to S^{1}$ on a closed orientable surface $M$, under what condition there exist a compact orientable 3-dimensional manifold $N$ with $\partial N = M$ and a submersion $G\colon N \to S^{1}$ such that $G|_{\partial N}=f$. We provide necessary and sufficient conditions for the existence of a non-singular extension of a circle-valued Morse function as the main theorem when a submersion on a collar neighborhood is given.

math.GT↗