The computation of the index of a Morse function at a critical point
A theoretical approach in computing the index of a Morse function at a critical point on a real non-singular hypersurface V is given. As a consequence the Euler characteristic of V is computed. In the case where the hypersurface is polynomial and compact, a procedure is given that finds a linear fun...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171288000870 |
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| _version_ | 1832554563170729984 |
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| author | Takis Sakkalis |
| author_facet | Takis Sakkalis |
| author_sort | Takis Sakkalis |
| collection | DOAJ |
| description | A theoretical approach in computing the index of a Morse function at a critical point on a real non-singular hypersurface V is given. As a consequence the Euler characteristic of V is computed. In the case where the hypersurface is polynomial and compact, a procedure is given that finds a linear function ℓ, whose restriction ℓ|V, is a Morse function on V. |
| format | Article |
| id | doaj-art-48eae78a080a4855ad20fe1e34f39c82 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-48eae78a080a4855ad20fe1e34f39c822025-02-03T05:51:03ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111472172610.1155/S0161171288000870The computation of the index of a Morse function at a critical pointTakis Sakkalis0Department of Mathematical Sciences, New Mexico State University, Las Cruces 88003, NM, USAA theoretical approach in computing the index of a Morse function at a critical point on a real non-singular hypersurface V is given. As a consequence the Euler characteristic of V is computed. In the case where the hypersurface is polynomial and compact, a procedure is given that finds a linear function ℓ, whose restriction ℓ|V, is a Morse function on V.http://dx.doi.org/10.1155/S0161171288000870Morse functioncritical pointindex. |
| spellingShingle | Takis Sakkalis The computation of the index of a Morse function at a critical point International Journal of Mathematics and Mathematical Sciences Morse function critical point index. |
| title | The computation of the index of a Morse function at a critical point |
| title_full | The computation of the index of a Morse function at a critical point |
| title_fullStr | The computation of the index of a Morse function at a critical point |
| title_full_unstemmed | The computation of the index of a Morse function at a critical point |
| title_short | The computation of the index of a Morse function at a critical point |
| title_sort | computation of the index of a morse function at a critical point |
| topic | Morse function critical point index. |
| url | http://dx.doi.org/10.1155/S0161171288000870 |
| work_keys_str_mv | AT takissakkalis thecomputationoftheindexofamorsefunctionatacriticalpoint AT takissakkalis computationoftheindexofamorsefunctionatacriticalpoint |