Deformations of smooth functions on 2-torus
Let $f$ be a Morse function on a smooth compact surface $M$ and $\mathcal{S}'(f)$ be the group of $f$-preserving diffeomorphisms of $M$ which are isotopic to the identity map. Let also $G(f)$ be a group of automorphisms of the Kronrod-Reeb graph of $f$ induced by elements from $\mathcal{S}'...
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2019-12-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
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| Online Access: | https://journals.onaft.edu.ua/index.php/geometry/article/view/1528 |
| _version_ | 1811228133973557248 |
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| author | Bohdan Feshchenko |
| author_facet | Bohdan Feshchenko |
| author_sort | Bohdan Feshchenko |
| collection | DOAJ |
| description | Let $f$ be a Morse function on a smooth compact surface $M$ and $\mathcal{S}'(f)$ be the group of $f$-preserving diffeomorphisms of $M$ which are isotopic to the identity map. Let also $G(f)$ be a group of automorphisms of the Kronrod-Reeb graph of $f$ induced by elements from $\mathcal{S}'(f)$, and $\Delta'$ be the subgroup of $\mathcal{S}'(f)$ consisting of diffeomorphisms which trivially act on the graph of $f$ and are isotopic to the identity map. The group $\pi_0\mathcal{S}'(f)$ can be viewed as an analogue of a mapping class group for $f$-preserved diffeomorphisms of $M$. The groups $\pi_0\Delta'(f)$ and $G(f)$ encode ``combinatorially trivial'' and ``combinatorially nontrivial'' counterparts of $\pi_0\mathcal{S}'(f)$ respectively. In the paper we compute groups $\pi_0\mathcal{S}'(f)$, $G(f)$, and $\pi_0\Delta'(f)$ for Morse functions on $2$-torus $T^2$. |
| first_indexed | 2024-04-12T09:53:26Z |
| format | Article |
| id | doaj.art-925e92eff11f4fa09324b9252c4b1b7c |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-04-12T09:53:26Z |
| publishDate | 2019-12-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-925e92eff11f4fa09324b9252c4b1b7c2022-12-22T03:37:47ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062019-12-01123305010.15673/tmgc.v12i3.15281528Deformations of smooth functions on 2-torusBohdan Feshchenko0Institute of Mathematics of NAS of UkraineLet $f$ be a Morse function on a smooth compact surface $M$ and $\mathcal{S}'(f)$ be the group of $f$-preserving diffeomorphisms of $M$ which are isotopic to the identity map. Let also $G(f)$ be a group of automorphisms of the Kronrod-Reeb graph of $f$ induced by elements from $\mathcal{S}'(f)$, and $\Delta'$ be the subgroup of $\mathcal{S}'(f)$ consisting of diffeomorphisms which trivially act on the graph of $f$ and are isotopic to the identity map. The group $\pi_0\mathcal{S}'(f)$ can be viewed as an analogue of a mapping class group for $f$-preserved diffeomorphisms of $M$. The groups $\pi_0\Delta'(f)$ and $G(f)$ encode ``combinatorially trivial'' and ``combinatorially nontrivial'' counterparts of $\pi_0\mathcal{S}'(f)$ respectively. In the paper we compute groups $\pi_0\mathcal{S}'(f)$, $G(f)$, and $\pi_0\Delta'(f)$ for Morse functions on $2$-torus $T^2$.https://journals.onaft.edu.ua/index.php/geometry/article/view/1528surface, isotopy, morse function, wreath product |
| spellingShingle | Bohdan Feshchenko Deformations of smooth functions on 2-torus Pracì Mìžnarodnogo Geometričnogo Centru surface, isotopy, morse function, wreath product |
| title | Deformations of smooth functions on 2-torus |
| title_full | Deformations of smooth functions on 2-torus |
| title_fullStr | Deformations of smooth functions on 2-torus |
| title_full_unstemmed | Deformations of smooth functions on 2-torus |
| title_short | Deformations of smooth functions on 2-torus |
| title_sort | deformations of smooth functions on 2 torus |
| topic | surface, isotopy, morse function, wreath product |
| url | https://journals.onaft.edu.ua/index.php/geometry/article/view/1528 |
| work_keys_str_mv | AT bohdanfeshchenko deformationsofsmoothfunctionson2torus |