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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 3, Pages 79–118 (Mi izv436)  

This article is cited in 20 scientific papers (total in 20 papers)

On braid monodromy factorizations

V. M. Kharlamova, Vik. S. Kulikovb

a University Louis Pasteur
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We introduce and develop a language of semigroups over the braid groups to study the braid monodromy factorizations (bmf's) of plane algebraic curves and other related objects. As an application, we give a new proof of Orevkov's theorem on the realization of bmf's over a disc by algebraic curves and show that the complexity of such a realization cannot be bounded in terms of the types of factors of the bmf. We also prove that the type of a bmf distinguishes Hurwitz curves with singularities of inseparable type up to $H$-isotopy and $J$-holomorphic cuspidal curves in $\mathbb{CP}^2$ up to symplectic isotopy.

DOI: https://doi.org/10.4213/im436

Full text: PDF file (4176 kB)
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English version:
Izvestiya: Mathematics, 2003, 67:3, 499–534

Bibliographic databases:

Document Type: Article
UDC: 512.772.1+514.756.44
MSC: 14E20
Received: 23.01.2003

Citation: V. M. Kharlamov, Vik. S. Kulikov, “On braid monodromy factorizations”, Izv. RAN. Ser. Mat., 67:3 (2003), 79–118; Izv. Math., 67:3 (2003), 499–534

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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. Vik. S. Kulikov, “A factorization formula for the full twist of double the number of strings”, Izv. Math., 68:1 (2004), 125–158  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Vik. S. Kulikov, D. Auroux, V. V. Shevchishin, “Regular homotopy of Hurwitz curves”, Izv. Math., 68:3 (2004), 521–542  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Auroux D., “A stable classification of Lefschetz fibrations”, Geom. Topol., 9 (2005), 203–217  crossref  mathscinet  zmath  isi  scopus
    4. McKay B., “Smooth projective planes”, Geom. Dedicata, 116:1 (2005), 157–202  crossref  mathscinet  zmath  isi  scopus
    5. 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
    6. 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
    7. Auroux D., “Some open questions about symplectic 4-manifolds, singular plane curves and braid group factorizations”, European Congress of Mathematics, 2005, 23–40  mathscinet  zmath  isi
    8. Vik. S. Kulikov, “Alexander polynomials of Hurwitz curves”, Izv. Math., 70:1 (2006), 69–86  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. Vik. S. Kulikov, “Hurwitz curves”, Russian Math. Surveys, 62:6 (2007), 1043–1119  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Vik. S. Kulikov, “Alexander modules of irreducible $C$-groups”, Izv. Math., 72:2 (2008), 305–344  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. Auroux D., Smith I., “Lefschetz pencils, branched covers and symplectic invariants”, Symplectic 4-manifolds and algebraic surfaces, Lecture Notes in Math., 1938, Springer, Berlin, 2008, 1–53  crossref  mathscinet  zmath  isi
    12. 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
    13. Vik. S. Kulikov, “Factorization semigroups and irreducible components of the Hurwitz space”, Izv. Math., 75:4 (2011), 711–748  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. Degtyarev A., “Hurwitz equivalence of braid monodromies and extremal elliptic surfaces”, Proc London Math Soc, 103:6 (2011), 1083–1120  crossref  mathscinet  zmath  isi  scopus
    15. Enrique Artal Bartolo, José Ignacio Cogolludo Agustín, Jorge Ortigas-Galindo, “Computation-free presentation of the fundamental group of generic (p,q)–torus curves”, Algebr. Geom. Topol, 12:3 (2012), 1265  crossref  mathscinet  zmath  isi  scopus
    16. Vik. S. Kulikov, V. M. Kharlamov, “Covering semigroups”, Izv. Math., 77:3 (2013), 594–626  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. H. Endo, S. Kamada, “Chart description for hyperelliptic Lefschetz fibrations and their stabilization”, Topology Appl., 196:B (2015), 416–430  crossref  mathscinet  zmath  isi  scopus
    18. Auroux D., “Factorizations in Sl(2, Z) and Simple Examples of Inequivalent Stein Fillings”, J. Symplectic Geom., 13:2 (2015), 261–277  crossref  mathscinet  zmath  isi  elib  scopus
    19. Endo H., Kamada S., “Counting Dirac Braid Relators and Hyperelliptic Lefschetz Fibrations”, Trans. London Math. Soc., 4:1 (2017), 72–99  crossref  mathscinet  zmath  isi  scopus
    20. Artal Bartolo E. Ignacio Cogolludo-Agustin J., “Some Open Questions on Arithmetic Zariski Pairs”, Singularities in Geometry, Topology, Foliations and Dynamics: a Celebration of the 60Th Birthday of Jose Seade, Trends in Mathematics, ed. CisnerosMolina J. Le D. Oka M. Snoussi J., Springer International Publishing Ag, 2017, 31–54  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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