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Tr. Mat. Inst. Steklova, 2001, Volume 235, Pages 181–210 (Mi tm244)  

This article is cited in 2 scientific papers (total in 2 papers)

Counterexamples to the “Jacobian Conjecture at Infinity”

S. Yu. Orevkov


Abstract: Earlier, the author constructed an example of an open complex surface $U$, a smooth compact rational curve $L\subset U$ with the self-intersection index $+1$, and a holomorphic immersion $f:U\setminus L\to\mathbb C^2$ that is meromorphic on $U$ but is not an embedding (if $U\subset \mathbb C\mathrm P^2$, then such an immersion can be extended to a counterexample to the Jacobian conjecture). In this paper, an analogous example is constructed with the property that $f|_{\partial U}$ is an immersion of a 3-sphere in $\mathbb C^2$ which is regularly homotopic to an embedding. The map $f$ cannot be extended to a counterexample to the Jacobian conjecture, which is proved by the analysis of the coefficients of polynomials.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 235, 173–201

Bibliographic databases:
UDC: 512.77
Received in June 2001

Citation: S. Yu. Orevkov, “Counterexamples to the “Jacobian Conjecture at Infinity””, Analytic and geometric issues of complex analysis, Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin, Tr. Mat. Inst. Steklova, 235, Nauka, MAIK Nauka/Inteperiodika, M., 2001, 181–210; Proc. Steklov Inst. Math., 235 (2001), 173–201

Citation in format AMSBIB
\Bibitem{Ore01}
\by S.~Yu.~Orevkov
\paper Counterexamples to the ``Jacobian Conjecture at Infinity''
\inbook Analytic and geometric issues of complex analysis
\bookinfo Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin
\serial Tr. Mat. Inst. Steklova
\yr 2001
\vol 235
\pages 181--210
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm244}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1886583}
\zmath{https://zbmath.org/?q=an:1009.14012}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 235
\pages 173--201


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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. A. V. Domrina, “A Restriction on the Combinatorial Structure of Counterexamples to the Jacobian Conjecture at Infinity”, Proc. Steklov Inst. Math., 253 (2006), 51–56  mathnet  crossref  mathscinet  elib
    2. Zoladek H., “An application of Newton–Puiseux charts to the Jacobian problem”, Topology, 47:6 (2008), 431–469  crossref  mathscinet  zmath  isi  scopus
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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