A~combinatorial invariant of gradient-like flows on a~connected sum of $\mathbb{S}^{n-1}\times\mathbb{S}^1$
Sbornik. Mathematics, Tome 214 (2023) no. 5, pp. 703-731
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We obtain necessary and sufficient conditions for the topological equivalence of gradient-like flows without heteroclinic intersections defined on the connected sum of a finite number of manifolds homeomorphic to $\mathbb{S}^{n-1}\times \mathbb{S}^1$, $n\geq 3$. For $n>3$, this result extends substantially the class of manifolds such that structurally stable systems on these manifolds admit a topological classification.
Bibliography: 36 titles.
Keywords:
topological classification, gradient-like flow, Morse-Smale flow.
@article{SM_2023_214_5_a3,
author = {V. Z. Grines and E. Ya. Gurevich},
title = {A~combinatorial invariant of gradient-like flows on a~connected sum of $\mathbb{S}^{n-1}\times\mathbb{S}^1$},
journal = {Sbornik. Mathematics},
pages = {703--731},
publisher = {mathdoc},
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year = {2023},
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V. Z. Grines; E. Ya. Gurevich. A~combinatorial invariant of gradient-like flows on a~connected sum of $\mathbb{S}^{n-1}\times\mathbb{S}^1$. Sbornik. Mathematics, Tome 214 (2023) no. 5, pp. 703-731. http://geodesic.mathdoc.fr/item/SM_2023_214_5_a3/