The relative cup-length in local Morse cohomology
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913219995500544 |
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| author | Rot, Thomas O. Starostka, Maciej Waterstraat, Nils |
| author_facet | Rot, Thomas O. Starostka, Maciej Waterstraat, Nils |
| contents | Local Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds $M$. We show that local Morse cohomology is a module over the cohomology of the isolating neighborhood, which allows us to define a cup-length relative to the cohomology of the isolating neighborhood that gives a lower bound on the number of critical points of functions on $M$ that are not necessarily Morse. Finally, we illustrate by an example that this lower bound can indeed be stronger than the lower bound given by the absolute cup-length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_10309 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The relative cup-length in local Morse cohomology Rot, Thomas O. Starostka, Maciej Waterstraat, Nils Geometric Topology 58E05, 55N45, 58C05 Local Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds $M$. We show that local Morse cohomology is a module over the cohomology of the isolating neighborhood, which allows us to define a cup-length relative to the cohomology of the isolating neighborhood that gives a lower bound on the number of critical points of functions on $M$ that are not necessarily Morse. Finally, we illustrate by an example that this lower bound can indeed be stronger than the lower bound given by the absolute cup-length. |
| title | The relative cup-length in local Morse cohomology |
| topic | Geometric Topology 58E05, 55N45, 58C05 |
| url | https://arxiv.org/abs/2212.10309 |