Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$
The present paper investigates Heegaard diagrams of non-orientable closed $3$-manifolds, i.e. a non-orienable closed surface together with two sets of meridian disks of both handlebodies. It is found all possible non-orientable genus $2$ Heegaard diagrams of complexity less than $6$. Topological p...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2020-12-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
| Subjects: | |
| Online Access: | https://journals.onaft.edu.ua/index.php/geometry/article/view/1779 |
| _version_ | 1818531381769142272 |
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| author | Christian Hatamian Alexandr Prishlyak |
| author_facet | Christian Hatamian Alexandr Prishlyak |
| author_sort | Christian Hatamian |
| collection | DOAJ |
| description | The present paper investigates Heegaard diagrams of non-orientable closed $3$-manifolds, i.e. a non-orienable closed surface together with two sets of meridian disks of both handlebodies.
It is found all possible non-orientable genus $2$ Heegaard diagrams of complexity less than $6$.
Topological properties of Morse flows on closed smooth non-orientable $3$-manifolds are described.
Normalized Heegaard diagrams are furhter used for classification Morse flows with a minimal number of singular points and singular trajectories |
| first_indexed | 2024-12-11T17:31:44Z |
| format | Article |
| id | doaj.art-d32f13ed9a8d49be96efac896e47297b |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-12-11T17:31:44Z |
| publishDate | 2020-12-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-d32f13ed9a8d49be96efac896e47297b2022-12-22T00:56:47ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062020-12-01133334810.15673/tmgc.v13i3.17791779Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$Christian HatamianAlexandr PrishlyakThe present paper investigates Heegaard diagrams of non-orientable closed $3$-manifolds, i.e. a non-orienable closed surface together with two sets of meridian disks of both handlebodies. It is found all possible non-orientable genus $2$ Heegaard diagrams of complexity less than $6$. Topological properties of Morse flows on closed smooth non-orientable $3$-manifolds are described. Normalized Heegaard diagrams are furhter used for classification Morse flows with a minimal number of singular points and singular trajectorieshttps://journals.onaft.edu.ua/index.php/geometry/article/view/1779topological equivalenceheegaard diagrammorse flow |
| spellingShingle | Christian Hatamian Alexandr Prishlyak Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$ Pracì Mìžnarodnogo Geometričnogo Centru topological equivalence heegaard diagram morse flow |
| title | Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$ |
| title_full | Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$ |
| title_fullStr | Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$ |
| title_full_unstemmed | Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$ |
| title_short | Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$ |
| title_sort | heegaard diagrams and optimal morse flows on non orientable 3 manifolds of genus 1 and genus 2 |
| topic | topological equivalence heegaard diagram morse flow |
| url | https://journals.onaft.edu.ua/index.php/geometry/article/view/1779 |
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