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Mat. Zametki, 2012, Volume 92, Issue 2, Pages 241–261 (Mi mz9140)  

This article is cited in 10 scientific papers (total in 10 papers)

The Topology of Spaces of Morse Functions on Surfaces

E. A. Kudryavtseva

M. V. Lomonosov Moscow State University

Abstract: The topology of the space $F=F(M)$ of Morse functions on a compact smooth orientable two-dimensional surface $M$ is studied.

Keywords: Morse function on a surface, framed Morse function, space of Morse functions, smooth compact orientable surface, homotopy equivalence

DOI: https://doi.org/10.4213/mzm9140

Full text: PDF file (669 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 92:2, 219–236

Bibliographic databases:

UDC: 515.164.174+515.164.22+515.122.55
Received: 27.04.2011

Citation: E. A. Kudryavtseva, “The Topology of Spaces of Morse Functions on Surfaces”, Mat. Zametki, 92:2 (2012), 241–261; Math. Notes, 92:2 (2012), 219–236

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kravchenko A., Maksymenko S., “Automorphisms of Kronrod-Reeb Graphs of Morse Functions on Compact Surfaces”, Eur. J. Math.  crossref  mathscinet  isi
    2. E. A. Kudryavtseva, “Special framed Morse functions on surfaces”, Moscow University Mathematics Bulletin, 67:4 (2012), 151–157  mathnet  crossref  mathscinet
    3. E. A. Kudryavtseva, “On the homotopy type of spaces of Morse functions on surfaces”, Sb. Math., 204:1 (2013), 75–113  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Kudryavtseva E.A., “Topology of the spaces of functions with prescribed singularities on surfaces”, Dokl. Math., 93:3 (2016), 264–266  crossref  mathscinet  zmath  isi  elib  scopus
    5. Maksymenko S., “Symplectomorphisms of Surfaces Preserving a Smooth Function, i”, Topology Appl., 235 (2018), 275–289  crossref  mathscinet  zmath  isi  scopus
    6. Maksymenko S., “Deformations of Functions on Surfaces By Isotopic to the Identity Diffeomorphisms”, Topology Appl., 282 (2020), 107312  crossref  mathscinet  isi
    7. Hladysh B.I., Prishlyak O.O., “Deformations in the General Position of the Optimal Functions on Oriented Surfaces With Boundary”, Ukr. Math. J., 71:8 (2020), 1173–1185  crossref  mathscinet  isi
    8. Khohliyk O., Maksymenko S., “Diffeomorphisms Preserving Morse-Bott Functions”, Indag. Math.-New Ser., 31:2 (2020), 185–203  crossref  mathscinet  isi
    9. Kravchenko A., Feshchenko B., “Automorphisms of Kronrod-Reeb Graphs of Morse Functions on 2-Torus”, Methods Funct. Anal. Topol., 26:1 (2020), 88–96  crossref  mathscinet  isi
    10. Anna Kravchenko, Sergiy Maksymenko, “Automorphisms of cellular divisions of $2$-sphere induced by functions with isolated critical points”, Zhurn. matem. fiz., anal., geom., 16:2 (2020), 138–160  mathnet  crossref
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