On reconstructing Morse-Bott functions with prescribed preimages on $3$-dimensional manifolds and conditions for the reconstruction
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909666241413120 |
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| author | Kitazawa, Naoki |
| author_facet | Kitazawa, Naoki |
| contents | We present conditions for reconstruction of Morse-Bott functions with prescribed preimages on $3$-dimensional manifolds. The present work strengthens a previous result for the Morse function case by the author and present a related example as another result. This shows a new result on reconstruction of nice smooth functions such that preimages are as prescribed. Such a study has been fundamental, natural, and surprisingly, founded recently, in 2006, by Sharko. Reconstruction of nice smooth functions on closed surfaces has been followed by Masumoto-Saeki, for example, and later, Gelbukh, Marzantowicz, Michalak, and so on, are studying Morse function cases further. The author has started explicit studies for $3$-dimensional cases respecting topologies of preimages of single points and obtained several results. We add another result on this. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On reconstructing Morse-Bott functions with prescribed preimages on $3$-dimensional manifolds and conditions for the reconstruction Kitazawa, Naoki Geometric Topology We present conditions for reconstruction of Morse-Bott functions with prescribed preimages on $3$-dimensional manifolds. The present work strengthens a previous result for the Morse function case by the author and present a related example as another result. This shows a new result on reconstruction of nice smooth functions such that preimages are as prescribed. Such a study has been fundamental, natural, and surprisingly, founded recently, in 2006, by Sharko. Reconstruction of nice smooth functions on closed surfaces has been followed by Masumoto-Saeki, for example, and later, Gelbukh, Marzantowicz, Michalak, and so on, are studying Morse function cases further. The author has started explicit studies for $3$-dimensional cases respecting topologies of preimages of single points and obtained several results. We add another result on this. |
| title | On reconstructing Morse-Bott functions with prescribed preimages on $3$-dimensional manifolds and conditions for the reconstruction |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2501.05992 |