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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 1, Pages 123–158 (Mi izv468)  

This article is cited in 6 scientific papers (total in 6 papers)

A factorization formula for the full twist of double the number of strings

Vik. S. Kulikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We give a formula for factorizing the full twist in the braid group $\operatorname{Br}_{2m}$ in terms of four factorizations of the full twist in$\operatorname{Br}_{m}$. This formula is used to construct a symplectic 4-manifold $X$ and two regularly homotopic generic coverings $f_i\colon X\to\mathbb C\mathbb P^2$ branched along cuspidal Hurwitz curves $\overline H_i\subset\mathbb C\mathbb P^2$ (without negative nodes) having different braid monodromy factorization types. The class of fundamental groups of complements of affine plane Hurwitz curves is described in terms of generators and defining relations.

DOI: https://doi.org/10.4213/im468

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English version:
Izvestiya: Mathematics, 2004, 68:1, 125–158

Bibliographic databases:

UDC: 512.722.1+514.756.44
MSC: 14E20
Received: 26.08.2003

Citation: Vik. S. Kulikov, “A factorization formula for the full twist of double the number of strings”, Izv. RAN. Ser. Mat., 68:1 (2004), 123–158; Izv. Math., 68:1 (2004), 125–158

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. O. V. Kulikova, “On the fundamental groups of the complements of Hurwitz curves”, Izv. Math., 69:1 (2005), 123–130  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. 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
    3. Vik. S. Kulikov, “Alexander polynomials of Hurwitz curves”, Izv. Math., 70:1 (2006), 69–86  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Vik. S. Kulikov, “Hurwitz curves”, Russian Math. Surveys, 62:6 (2007), 1043–1119  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Vik. S. Kulikov, “Alexander modules of irreducible $C$-groups”, Izv. Math., 72:2 (2008), 305–344  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Bauer I., Catanese F., Pignatelli R., “Surfaces of General Type with Geometric Genus Zero: a Survey”, Complex and Differential Geometry, Springer Proceedings in Mathematics, 8, eds. Ebeling W., Hulek K., Smoczyk K., Springer-Verlag Berlin, 2011, 1–48  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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