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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 3, Pages 91–114 (Mi izv487)  

This article is cited in 9 scientific papers (total in 9 papers)

Regular homotopy of Hurwitz curves

Vik. S. Kulikova, D. Aurouxb, V. V. Shevchishinc

a Steklov Mathematical Institute, Russian Academy of Sciences
b Massachusetts Institute of Technology
c Ruhr-Universität Bochum

Abstract: We prove that any two irreducible cuspidal Hurwitz curves $C_0$ and $C_1$ (or, more generally, two curves with $A$-type singularities) in the Hirzebruch surface $\boldsymbol F_N$ with the same homology classes and sets of singularities are regular homotopic. Moreover, they are symplectically regular homotopic if $C_0$ and $C_1$ are symplectic with respect to a compatible symplectic form.

DOI: https://doi.org/10.4213/im487

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English version:
Izvestiya: Mathematics, 2004, 68:3, 521–542

Bibliographic databases:

Document Type: Article
UDC: 512.722.1+514.756.44
MSC: 32Q65, 53D05, 58D27, 14H10
Received: 13.01.2004

Citation: Vik. S. Kulikov, D. Auroux, V. V. Shevchishin, “Regular homotopy of Hurwitz curves”, Izv. RAN. Ser. Mat., 68:3 (2004), 91–114; Izv. Math., 68:3 (2004), 521–542

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. 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
    2. Vik. S. Kulikov, “Hurwitz curves”, Russian Math. Surveys, 62:6 (2007), 1043–1119  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Auroux D., Katzarkov L., “A degree doubling formula for braid monodromies and lefschetz pencils”, Pure Appl. Math. Q., 4:2 (2008), 237–318  crossref  mathscinet  zmath  isi  elib
    4. 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
    5. Geng A., “Two Surfaces in D-4 Bounded By the Same Knot”, J Symplectic Geom, 9:2 (2011), 119–122  crossref  mathscinet  zmath  isi  elib  scopus
    6. Degtyarev A., Salepci N., “Products of Pairs of Dehn Twists and Maximal Real Lefschetz Fibrations”, Nagoya Math. J., 210 (2013), 83–132  crossref  mathscinet  zmath  isi  scopus
    7. Cao Ch., Gallup N., Hayden K., Sabloff J.M., “Topologically Distinct Lagrangian and Symplectic Fillings”, Math. Res. Lett., 21:1 (2014), 85–99  crossref  mathscinet  zmath  isi  scopus
    8. 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
    9. Baykur R.I., Van Horn-Morris J., “Fillings of Genus-1 Open Books and 4-Braids”, Int. Math. Res. Notices, 2018, no. 5, 1329–1346  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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