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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 1, Pages 153–166 (Mi izv375)  

This article is cited in 5 scientific papers (total in 5 papers)

Lefschetz pencils, Morse functions, and Lagrangian embeddings of the Klein bottle

S. Yu. Nemirovski

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: It is shown that the mod 2 homology class represented by a Lagrangian Klein bottle in a complex algebraic surface is non-zero. In particular, the Klein bottle does not admit a Lagrangian embedding into the standard symplectic four-space.

DOI: https://doi.org/10.4213/im375

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English version:
Izvestiya: Mathematics, 2002, 66:1, 151–164

Bibliographic databases:

Document Type: Article
UDC: 513.8+515.1
MSC: 53D12, 14D05, 32F17
Received: 05.09.2001

Citation: S. Yu. Nemirovski, “Lefschetz pencils, Morse functions, and Lagrangian embeddings of the Klein bottle”, Izv. RAN. Ser. Mat., 66:1 (2002), 153–166; Izv. Math., 66:1 (2002), 151–164

Citation in format AMSBIB
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\by S.~Yu.~Nemirovski
\paper Lefschetz pencils, Morse functions, and Lagrangian embeddings of the Klein bottle
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 1
\pages 153--166
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\crossref{https://doi.org/10.4213/im375}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1917541}
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\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 1
\pages 151--164
\crossref{https://doi.org/10.1070/IM2002v066n01ABEH000375}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748484719}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mironov A. E., “On Hamiltonian-minimal and minimal Lagrangian submanifolds in $\mathbb C^n$ and $\mathbb CP^n$”, Dokl. Math., 69:3 (2004), 352–354  mathnet  mathscinet  zmath  isi
    2. A. E. Mironov, “New examples of Hamilton-minimal and minimal Lagrangian manifolds in $\mathbb C^n$ and $\mathbb C\mathrm P^n$”, Sb. Math., 195:1 (2004), 85–96  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. S. Yu. Nemirovski, “Homology class of a Lagrangian Klein bottle”, Izv. Math., 73:4 (2009), 689–698  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. V. Shevchishin, “Lagrangian embeddings of the Klein bottle and combinatorial properties of mapping class groups”, Izv. Math., 73:4 (2009), 797–859  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Nemirovski S., “Lagrangian Klein Bottles in $\mathbb R^{2n}$”, GAFA Geom. Funct. Anal., 19:3 (2009), 902–909  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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