Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits

The purpose of this study is to establish the topological properties of three-dimensional manifolds which admit Morse – Smale flows without fixed points (non-singular or NMS-flows) and give examples of such manifolds that are not lens spaces. Despite the fact that it is known that any such...

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Autor principal:	Shubin, Danila Denisovich
Formato:	article
Lenguaje:	EN RU
Publicado:	Saratov State University 2021
Materias:	nonsingular flows morse – smale flows Physics QC1-999
Acceso en línea:	https://doaj.org/article/a18d23ea600d4af0835a9d4b5f3357fe
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id	oai:doaj.org-article:a18d23ea600d4af0835a9d4b5f3357fe
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spelling	oai:doaj.org-article:a18d23ea600d4af0835a9d4b5f3357fe2021-11-30T10:45:19ZTopology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits0869-66322542-190510.18500/0869-6632-2021-29-6-863-868https://doaj.org/article/a18d23ea600d4af0835a9d4b5f3357fe2021-11-01T00:00:00Zhttps://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2021/11/shubin_863-868.pdfhttps://doaj.org/toc/0869-6632https://doaj.org/toc/2542-1905The purpose of this study is to establish the topological properties of three-dimensional manifolds which admit Morse – Smale flows without fixed points (non-singular or NMS-flows) and give examples of such manifolds that are not lens spaces. Despite the fact that it is known that any such manifold is a union of circular handles, their topology can be investigated additionally and refined in the case of a small number of orbits. For example, in the case of a flow with two non-twisted (having a tubular neighborhood homeomorphic to a solid torus) orbits, the topology of such manifolds is established exactly: any ambient manifold of an NMS-flow with two orbits is a lens space. Previously, it was believed that all prime manifolds admitting NMS-flows with at most three non-twisted orbits have the same topology. Methods. In this paper, we consider suspensions over Morse – Smale diffeomorphisms with three periodic orbits. These suspensions, in turn, are NMS-flows with three periodic trajectories. Universal coverings of the ambient manifolds of these flows and lens spaces are considered. Results. In this paper, we present a countable set of pairwise distinct simple 3-manifolds admitting NMS-flows with exactly three non-twisted orbits. Conclusion. From the results of this paper it follows that there is a countable set of pairwise distinct three-dimensional manifolds other than lens spaces, which refutes the previously published result that any simple orientable manifold admitting an NMS-flow with at most three orbits is lens space.Shubin, Danila DenisovichSaratov State Universityarticlenonsingular flowsmorse – smale flowsPhysicsQC1-999ENRUИзвестия высших учебных заведений: Прикладная нелинейная динамика, Vol 29, Iss 6, Pp 863-868 (2021)
institution	DOAJ
collection	DOAJ
language	EN RU
topic	nonsingular flows morse – smale flows Physics QC1-999
spellingShingle	nonsingular flows morse – smale flows Physics QC1-999 Shubin, Danila Denisovich Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits
description	The purpose of this study is to establish the topological properties of three-dimensional manifolds which admit Morse – Smale flows without fixed points (non-singular or NMS-flows) and give examples of such manifolds that are not lens spaces. Despite the fact that it is known that any such manifold is a union of circular handles, their topology can be investigated additionally and refined in the case of a small number of orbits. For example, in the case of a flow with two non-twisted (having a tubular neighborhood homeomorphic to a solid torus) orbits, the topology of such manifolds is established exactly: any ambient manifold of an NMS-flow with two orbits is a lens space. Previously, it was believed that all prime manifolds admitting NMS-flows with at most three non-twisted orbits have the same topology. Methods. In this paper, we consider suspensions over Morse – Smale diffeomorphisms with three periodic orbits. These suspensions, in turn, are NMS-flows with three periodic trajectories. Universal coverings of the ambient manifolds of these flows and lens spaces are considered. Results. In this paper, we present a countable set of pairwise distinct simple 3-manifolds admitting NMS-flows with exactly three non-twisted orbits. Conclusion. From the results of this paper it follows that there is a countable set of pairwise distinct three-dimensional manifolds other than lens spaces, which refutes the previously published result that any simple orientable manifold admitting an NMS-flow with at most three orbits is lens space.
format	article
author	Shubin, Danila Denisovich
author_facet	Shubin, Danila Denisovich
author_sort	Shubin, Danila Denisovich
title	Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits
title_short	Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits
title_full	Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits
title_fullStr	Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits
title_full_unstemmed	Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits
title_sort	topology of ambient manifolds of non-singular morse – smale flows with three periodic orbits
publisher	Saratov State University
publishDate	2021
url	https://doaj.org/article/a18d23ea600d4af0835a9d4b5f3357fe
work_keys_str_mv	AT shubindaniladenisovich topologyofambientmanifoldsofnonsingularmorsesmaleflowswiththreeperiodicorbits
_version_	1718406700735660032

Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits

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