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Matematicheskie Zametki, 2024, Volume 116, Issue 1, Pages 45–66
DOI: https://doi.org/10.4213/mzm14151 (Mi mzm14151) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Kirby diagram of polar flows on four-dimensional manifolds

E. Ya. Gurevich, I. A. Saraev

National Research University – Higher School of Economics in Nizhny Novgorod
Full-text PDF (773 kB) Citations (3) English version article
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DOI: https://doi.org/10.4213/mzm14151
Abstract: We solve the topological classification problem for polar flows on closed four-dimensional manifolds whose set of saddle equilibrium states consists only of points having two-dimensional stable and unstable manifolds. It is shown that the Kirby diagram, which is a framed link on a sphere intersecting the flow trajectories, is a complete topological invariant for such flows.
Keywords: polar flow, gradient-like flow, structurally stable flow, topological classification, Kirby diagram.
Funding agency Grant number
Russian Science Foundation 21-11-00010
National Research University Higher School of Economics 23-00-028
This work was supported by the grant of the Russian Science Foundation no. 21-11-00010, https://rscf.ru/en/project/21-11-00010/, except for Sec. 3, which was supported by the “Scientific Fund of the National Research University "Higher School of Economics” (NIU HSE) program in 2023, grant no. 23-00-028.
Received: 31.08.2023
Revised: 06.02.2024
Published: 01.07.2024
English version:
Mathematical Notes, 2024, Volume 116, Issue 1, Pages 40–57
DOI: https://doi.org/10.1134/S0001434624070046
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 37C15
Language: Russian
Citation: E. Ya. Gurevich, I. A. Saraev, “Kirby diagram of polar flows on four-dimensional manifolds”, Mat. Zametki, 116:1 (2024), 45–66; Math. Notes, 116:1 (2024), 40–57
Citation in format AMSBIB
\Bibitem{GurSar24}
\by E.~Ya.~Gurevich, I.~A.~Saraev
\paper Kirby diagram of polar flows on four-dimensional manifolds
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 1
\pages 45--66
\mathnet{http://mi.mathnet.ru/mzm14151}
\crossref{https://doi.org/10.4213/mzm14151}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 1
\pages 40--57
\crossref{https://doi.org/10.1134/S0001434624070046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85203472599}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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