Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold
This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface M which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by Ω(M). Firstly, we've obtained the to...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2017 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2017
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148582 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold / B.I. Hladysh, A.O. Prishlyak // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-148582 |
|---|---|
| record_format |
dspace |
| spelling |
Hladysh, B.I. Prishlyak, A.O. 2019-02-18T16:14:02Z 2019-02-18T16:14:02Z 2017 Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold / B.I. Hladysh, A.O. Prishlyak // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 57R45; 57R70 DOI:10.3842/SIGMA.2017.050 https://nasplib.isofts.kiev.ua/handle/123456789/148582 This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface M which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by Ω(M). Firstly, we've obtained the topological classification of above-mentioned functions in some neighborhood of their critical points. Secondly, we've constructed a chord diagram from the neighborhood of a critical level. Also the minimum number of critical points of such functions is being considered. And finally, the criterion of global topological equivalence of functions which belong to Ω(M) and have three critical points has been developed. This paper partially based on the talks of the first author given at the AUI’s seminars on Topology of functions with isolated critical points on the boundary of a 2-dimensional manifold (March 2–15, 2017, AUI, Vienna, Austria) and partially supported by the project between the Austrian Academy of Sciences and the National Academy of Sciences of Ukraine on Modern Problems in Noncommutative Astroparticle Physics and Categorian Quantum Theory. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold |
| spellingShingle |
Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold Hladysh, B.I. Prishlyak, A.O. |
| title_short |
Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold |
| title_full |
Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold |
| title_fullStr |
Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold |
| title_full_unstemmed |
Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold |
| title_sort |
topology of functions with isolated critical points on the boundary of a 2-dimensional manifold |
| author |
Hladysh, B.I. Prishlyak, A.O. |
| author_facet |
Hladysh, B.I. Prishlyak, A.O. |
| publishDate |
2017 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface M which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by Ω(M). Firstly, we've obtained the topological classification of above-mentioned functions in some neighborhood of their critical points. Secondly, we've constructed a chord diagram from the neighborhood of a critical level. Also the minimum number of critical points of such functions is being considered. And finally, the criterion of global topological equivalence of functions which belong to Ω(M) and have three critical points has been developed.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148582 |
| citation_txt |
Topology of Functions with Isolated Critical Points on the Boundary of a 2-Dimensional Manifold / B.I. Hladysh, A.O. Prishlyak // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 19 назв. — англ. |
| work_keys_str_mv |
AT hladyshbi topologyoffunctionswithisolatedcriticalpointsontheboundaryofa2dimensionalmanifold AT prishlyakao topologyoffunctionswithisolatedcriticalpointsontheboundaryofa2dimensionalmanifold |
| first_indexed |
2025-12-01T04:42:39Z |
| last_indexed |
2025-12-01T04:42:39Z |
| _version_ |
1850859320220057600 |