Topology of boundary special generic maps into Euclidean spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910101755920384 |
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| author | Iwakura, Koki |
| author_facet | Iwakura, Koki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topology of boundary special generic maps into Euclidean spaces Iwakura, Koki Geometric Topology 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. |
| title | Topology of boundary special generic maps into Euclidean spaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2508.01629 |