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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 2, Pages 89–120 (Mi izv285)  

This article is cited in 25 scientific papers (total in 25 papers)

Braid monodromy factorizations and diffeomorphism types

Vik. S. Kulikova, M. Teicherb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Bar-Ilan University, Department of Chemistry

Abstract: In this paper we prove that if two cuspidal plane curves $B_1$ and $B_2$ have equivalent braid monodromy factorizations, then $B_1$ and $B_2$ are smoothly isotopic in $\mathbb C\mathbb P^2$. As a consequence, we obtain that if $S_1$, $S_2$ are surfaces of general type embedded in a projective space by means of a multiple canonical class and if the discriminant curves (the branch curves) $B_1$$B_2$ of some smooth projections of $S_1$$S_2$ to $\mathbb{CP}^2$ have equivalent braid monodromy factorizations, then $S_1$ and $S_2$ are diffeomorphic (as real four-dimensional manifolds).

DOI: https://doi.org/10.4213/im285

Full text: PDF file (3089 kB)
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English version:
Izvestiya: Mathematics, 2000, 64:2, 311–341

Bibliographic databases:

Document Type: Article
MSC: 14E20
Received: 29.12.1998

Citation: Vik. S. Kulikov, M. Teicher, “Braid monodromy factorizations and diffeomorphism types”, Izv. RAN. Ser. Mat., 64:2 (2000), 89–120; Izv. Math., 64:2 (2000), 311–341

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. Kharlamov V., Kulikov V., “Diffeomorphisms, isotopies, and braid monodromy factorizations of plane cuspidal curves”, C. R. Acad. Sci. Paris Sér. I Math., 333:9 (2001), 855–859  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Amram M., Goldberg D., Teicher M., Vishne U., “The fundamental group of a Galois cover of $\mathbf C\roman P^1\times T$”, Algebr. Geom. Topol., 2 (2002), 403–432  crossref  mathscinet  zmath
    3. Kaplan S., Teicher M., “Identifying half-twists using randomized algorithm methods”, J. Symbolic Comput., 34:2 (2002), 91–103  crossref  mathscinet  zmath  isi  elib  scopus
    4. Teicher M., “Braid Monodromy Type invariants of surfaces and 4-manifolds”, Trends in Singularities, Trends in Mathematics, 2002, 215–222  mathscinet  zmath  isi
    5. V. M. Kharlamov, Vik. S. Kulikov, “On braid monodromy factorizations”, Izv. Math., 67:3 (2003), 499–534  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Garber D., “Plane curves and their fundamental groups: Generalizations of Uludaǧ's construction”, Algebr. Geom. Topol., 3 (2003), 593–622  crossref  mathscinet  zmath
    7. Ben-Itzhak T., Teicher M., “Hurwitz equivalence in the braid group $B_3$”, Internat. J. Algebra Comput., 13:3 (2003), 277–286  crossref  mathscinet  zmath  isi  elib  scopus
    8. Artal Bartolo E., Carmona Ruber J., Cogolludo Agustín J.I., “Braid monodromy and topology of plane curves”, Duke Math. J., 118:2 (2003), 261–278  crossref  mathscinet  zmath  isi  scopus
    9. Katzarkov L., “Monodromy invariants—from symplectic to smooth manifolds”, Monodromy and differential equations (Moscow, 2001), Acta Appl. Math., 75, no. 1-3, 2003, 85–103  crossref  mathscinet  zmath  isi  scopus
    10. 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
    11. 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
    12. Vik. S. Kulikov, “Hurwitz curves”, Russian Math. Surveys, 62:6 (2007), 1043–1119  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    13. Teicher M., Friedman M., “On non fundamental group equivalent surfaces”, Algebr. Geom. Topol., 8:1 (2008), 397–433  crossref  mathscinet  zmath  isi  scopus
    14. Friedman M., Teicher M., “On fundamental groups related to the Hirzebruch surface $F_1$”, Sci. China Ser. A, 51:4 (2008), 728–745  crossref  mathscinet  zmath  isi  elib  scopus
    15. Friedman M., Teicher M., “The regeneration of a 5-point”, Pure Appl. Math. Q., 4:2, part 1 (2008), 383–425  crossref  mathscinet  zmath  isi
    16. Amram M., Friedman M., Teicher M., “The fundamental group of the complement of the branch curve of the second Hirzebruch surface”, Topology, 48:1 (2009), 23–40  crossref  mathscinet  zmath  isi  scopus
    17. Amram M., Friedman M., Teicher M., “The fundamental group of the complement of the branch curve of $\mathbb{CP}^1\times T$”, Acta Math. Sin. (Engl. Ser.), 25:9 (2009), 1443–1458  crossref  mathscinet  zmath  isi  scopus
    18. Sia Charmaine, “Hurwitz equivalence in tuples of dihedral groups, dicyclic groups, and semidihedral groups”, Electron. J. Combin., 16:1 (2009), R95, 17 pp.  mathscinet  zmath  isi  elib
    19. Degtyarev A., “Zariski $k$-plets via dessins d'enfants”, Comment. Math. Helv., 84:3 (2009), 639–671  crossref  mathscinet  zmath  isi  scopus
    20. Eliyahu M., Garber D., Teicher M., “A conjugation-free geometric presentation of fundamental groups of arrangements”, Manuscripta Mathematica, 133:1–2 (2010), 247–271  crossref  mathscinet  zmath  isi  scopus
    21. Sheng-Li Tan, Stephen S.-T. Yau, Fei Ye, “A note on the topology of the complements of fiber-type line arrangements in ℂℙ2”, Pacific J. Math, 251:1 (2011), 207–218  crossref  mathscinet  zmath  isi  scopus
    22. Eliyahu M., Garber D., Teicher M., “A Conjugation-Free Geometric Presentation of Fundamental Groups of Arrangements II: Expansion and Some Properties”, Internat J Algebra Comput, 21:5 (2011), 775–792  crossref  mathscinet  zmath  isi  elib  scopus
    23. Degtyarev A., “Topology of plane algebraic curves: the algebraic approach”, Topology of Algebraic Varieties and Singularities, Contemporary Mathematics, 538, 2011, 137–161  crossref  mathscinet  zmath  isi
    24. Artal Bartolo E., Ignacio Cogolludo-Agustin J., Ortigas-Galindo J., “Kummer Covers and Braid Monodromy”, J. Inst. Math. Jussieu, 13:3 (2014), 633–670  crossref  mathscinet  zmath  isi  scopus
    25. Baumeister B., Gobet T., Roberts K., Wegener P., “On the Hurwitz action in finite Coxeter groups”, J. Group Theory, 20:1 (2017), 103–131  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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