Email this article Classification of nonsingular four-dimensional flows with a untwisted saddle orbit
- Authors: Galkin V.D.1, Pochinka O.V.1, Shubin D.D.1
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Affiliations:
- National Research University – Higher School of Economics in Nizhny Novgorod
- Issue: Vol 215, No 11 (2024)
- Pages: 65-91
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/279063
- DOI: https://doi.org/10.4213/sm10091
- ID: 279063
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Abstract
The topological equivalence of low-dimensional Morse–Smale flows without fixed point (NMS-flows) under assumptions of various generality is the subject of a number of publications. Starting from dimension 4, there are only few results on classification. However, it is known that there exists nonsingular flows with wildly embedded invariant saddle manifolds. In this paper the class of nonsingular Morse–Smale flows on closed orientable 4-manifolds with a unique saddle orbit which is, moreover, nontwisted, is considered. It is shown that the equivalence class of a certain knot embedded in $\mathbb S^2\times\mathbb S^1$ is a complete invariant of such a flow. Given a knot in $\mathbb S^2\times\mathbb S^1$, a standard representative in the class of flows under consideration is constructed. The supporting manifold of all such flows is shown to be the manifold $\mathbb S^3\times\mathbb S^1$.Bibliography: 24 titles.
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About the authors
Vladislav Dmitrievich Galkin
National Research University – Higher School of Economics in Nizhny Novgorod
Email: vgalkin@hse.ru
Olga Vital'evna Pochinka
National Research University – Higher School of Economics in Nizhny Novgorod
Email: olga-pochinka@yandex.ru
ORCID iD: 0000-0002-6587-5305
Doctor of physico-mathematical sciences, no status
Danila Denisovich Shubin
National Research University – Higher School of Economics in Nizhny Novgorod
Email: schub.danil@yandex.ru
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