Deformations of functions on surfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866913321291087872 |
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| author | Maksymenko, Sergiy |
| author_facet | Maksymenko, Sergiy |
| contents | The paper contains a review on recent progress in the deformational properties of smooth maps from compact surfaces $M$ to a one-dimensional manifold $P$. It covers description of homotopy types of stabilizers and orbits of a large class of smooth functions on surfaces obtained by the author, E. Kudryavtseva, B. Feshchenko, I. Kuznietsova, Yu. Soroka, A. Kravchenko. We also present here a new direct proof of the fact that for generic Morse maps the connected components their orbits are homotopy equivalent to finite products of circles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_13416 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Deformations of functions on surfaces Maksymenko, Sergiy Geometric Topology Algebraic Topology Differential Geometry Dynamical Systems 37J05, 57S05, 58B05 The paper contains a review on recent progress in the deformational properties of smooth maps from compact surfaces $M$ to a one-dimensional manifold $P$. It covers description of homotopy types of stabilizers and orbits of a large class of smooth functions on surfaces obtained by the author, E. Kudryavtseva, B. Feshchenko, I. Kuznietsova, Yu. Soroka, A. Kravchenko. We also present here a new direct proof of the fact that for generic Morse maps the connected components their orbits are homotopy equivalent to finite products of circles. |
| title | Deformations of functions on surfaces |
| topic | Geometric Topology Algebraic Topology Differential Geometry Dynamical Systems 37J05, 57S05, 58B05 |
| url | https://arxiv.org/abs/2105.13416 |