About non-uniqueness when removing closed orbits in Morse-Smale vector fields
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909334221357056 |
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| author | Bannwart, Clemens |
| author_facet | Bannwart, Clemens |
| contents | Given a Morse-Smale vector field on a smooth manifold, Franks described how one can replace a closed orbit of index $k$ by two rest points of index $k+1$ and $k$, using a local perturbation. Combined with classical results about gradient-like vector fields, this gives a method of assigning different topological or algebraic structures to Morse-Smale vector fields. We show that there are multiple non-equivalent ways of following this procedure and illustrate this non-uniqueness in various examples. We describe the consequences of this non-uniqueness to the endeavour of assigning CW complexes or chain complexes to Morse-Smale vector fields in a canonical way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | About non-uniqueness when removing closed orbits in Morse-Smale vector fields Bannwart, Clemens Algebraic Topology 57R25, 37D15 Given a Morse-Smale vector field on a smooth manifold, Franks described how one can replace a closed orbit of index $k$ by two rest points of index $k+1$ and $k$, using a local perturbation. Combined with classical results about gradient-like vector fields, this gives a method of assigning different topological or algebraic structures to Morse-Smale vector fields. We show that there are multiple non-equivalent ways of following this procedure and illustrate this non-uniqueness in various examples. We describe the consequences of this non-uniqueness to the endeavour of assigning CW complexes or chain complexes to Morse-Smale vector fields in a canonical way. |
| title | About non-uniqueness when removing closed orbits in Morse-Smale vector fields |
| topic | Algebraic Topology 57R25, 37D15 |
| url | https://arxiv.org/abs/2410.02363 |