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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 1, Pages 125–132 (Mi izv626)  

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

On the fundamental groups of the complements of Hurwitz curves

O. V. Kulikova

M. V. Lomonosov Moscow State University

Abstract: It is proved that the commutator subgroup of the fundamental group of the complement of any plane affine irreducible Hurwitz curve (or any plane affine irreducible pseudoholomorphic curve) is finitely presented. It is shown that there is a Hurwitz curve (resp. pseudoholomorphic curve) in $\mathbb{CP}^2$ such that the fundamental group of its complement is non-Hopfian and, therefore, this group is not residually finite. We also prove the existence of an irreducible non-singular algebraic curve $C\subset\mathbb C^2$ and a bidisc $D\subset\mathbb C^2$ such that the fundamental group $\pi_1(D\setminus C)$ is non-Hopfian.

DOI: https://doi.org/10.4213/im626

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English version:
Izvestiya: Mathematics, 2005, 69:1, 123–130

Bibliographic databases:

UDC: 514.756.44+512.543.16
MSC: 14F35, 20F34, 57M05
Received: 31.08.2004

Citation: O. V. Kulikova, “On the fundamental groups of the complements of Hurwitz curves”, Izv. RAN. Ser. Mat., 69:1 (2005), 125–132; Izv. Math., 69:1 (2005), 123–130

Citation in format AMSBIB
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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. G.-M. Greuel, Vik. S. Kulikov, “On symplectic coverings of the projective plane”, Izv. Math., 69:4 (2005), 667–701  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Vik. S. Kulikov, “Alexander polynomials of Hurwitz curves”, Izv. Math., 70:1 (2006), 69–86  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Vik. S. Kulikov, “Hurwitz curves”, Russian Math. Surveys, 62:6 (2007), 1043–1119  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Vik. S. Kulikov, “Alexander modules of irreducible $C$-groups”, Izv. Math., 72:2 (2008), 305–344  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Aschenbrenner M., Friedl S., Wilton H., 3-Manifold Groups, Ems Series of Lectures in Mathematics, Eur. Math. Soc., 2015  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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