Topology of boundary special generic maps into Euclidean spaces

Koki Iwakura

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arXiv · 2508.01629

Topology of boundary special generic maps into Euclidean spaces

Koki Iwakura

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Abstract

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.

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Koki Iwakura. 2025-08-03. Topology of boundary special generic maps into Euclidean spaces. https://arxiv.org/abs/2508.01629

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