Non-singular extensions of horizontal stable fold maps from surfaces to the plane
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911565614153728 |
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| author | Iwakura, Koki |
| author_facet | Iwakura, Koki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-singular extensions of horizontal stable fold maps from surfaces to the plane Iwakura, Koki Geometric Topology 58K05, 57K20, 57R45 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. |
| title | Non-singular extensions of horizontal stable fold maps from surfaces to the plane |
| topic | Geometric Topology 58K05, 57K20, 57R45 |
| url | https://arxiv.org/abs/2410.22693 |