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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.18944 |
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| _version_ | 1866913627216281600 |
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| author | Feshchenko, Bohdan |
| author_facet | Feshchenko, Bohdan |
| contents | This article is devoted to the study of a certain class of smooth circle-valued functions on a cylinder $S^1\times [0,1]$, a torus $T^2$, a disk $D^2$ and a sphere $S^2$ which is a generalization of Morse-Bott functions without saddles. We established a "normal form" for functions from this class, namely, we proved that any such function $f$ can be presented in the form $f = \varkappa\circ f_0\circ h^{-1}$, where $f_0$ is the ``simplest'' Morse function on the given surface for some diffeomorphism $h$ and a smooth function $\varkappa$ satisfying some natural conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normal forms of functions with degenerate singularities on surfaces equipped with semi-free circle actions Feshchenko, Bohdan Geometric Topology This article is devoted to the study of a certain class of smooth circle-valued functions on a cylinder $S^1\times [0,1]$, a torus $T^2$, a disk $D^2$ and a sphere $S^2$ which is a generalization of Morse-Bott functions without saddles. We established a "normal form" for functions from this class, namely, we proved that any such function $f$ can be presented in the form $f = \varkappa\circ f_0\circ h^{-1}$, where $f_0$ is the ``simplest'' Morse function on the given surface for some diffeomorphism $h$ and a smooth function $\varkappa$ satisfying some natural conditions. |
| title | Normal forms of functions with degenerate singularities on surfaces equipped with semi-free circle actions |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2412.18944 |