Denis Auroux - Papers

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These articles are available in PDF format. The version posted here may differ from the final published version.

  1. Asymptotically holomorphic families of symplectic submanifolds.
    Geom. Funct. Anal. 7 (1997), 971-995.   (Publisher web site)
  2. Symplectic 4-manifolds as branched coverings of CP2.
    Inventiones Math. 139 (2000), 551-602.   (Publisher web site)
  3. Branched coverings of CP2 and invariants of symplectic 4-manifolds.
    (with L. Katzarkov)
    Inventiones Math. 142 (2000), 631-673.   (Publisher web site)
  4. Symplectic maps to projective spaces and symplectic invariants.
    Proceedings of the 7th Gökova Geometry-Topology Conference (2000).
    Turkish J. Math. 25 (2001), 1-42.   (arXiv: math.GT/0007130)   (Publisher web site)
  5. Estimated transversality in symplectic geometry and projective maps.
    In "Symplectic Geometry and Mirror Symmetry", Proceedings of the 4th KIAS International Conference, Seoul (2000), World Scientific, Singapore, 2001, 1-30.   (arXiv: math.SG/0010052)
  6. Symplectic hypersurfaces in the complement of an isotropic submanifold.
    (with D. Gayet and J.-P. Mohsen)
    Math. Ann. 321 (2001), 739-754.   (Publisher web site)
  7. A remark about Donaldson's construction of symplectic submanifolds.
    J. Symplectic Geom. 1 (2002), 647-658.   (arXiv: math.DG/0204286)   (Publisher web site)
  8. Fiber sums of genus 2 Lefschetz fibrations.
    Proceedings of the 9th Gökova Geometry-Topology Conference (2002).
    Turkish J. Math. 27 (2003), 1-10.   (arXiv: math.GT/0204285)   (Publisher web site)
  9. Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves.
    (with S. K. Donaldson and L. Katzarkov)
    Math. Ann. 326 (2003), 185-203.   (arXiv: math.GT/0206005)   (Publisher web site)
  10. Fundamental groups of complements of plane curves and symplectic invariants.
    (with S. K. Donaldson, L. Katzarkov, M. Yotov)
    Topology 43 (2004), 1285-1318.   (arXiv: math.GT/0203183)   (Publisher web site)
  11. Regular homotopy of Hurwitz curves.
    (with V. S. Kulikov and V. V. Shevchishin)
    Izv. Math. 68 (2004), 521-542.   (arXiv: math.SG/0401172)   (Publisher web site)
  12. A stable classification of Lefschetz fibrations.
    Geom. Topol. 9 (2005), 203-217.   (arXiv: math.GT/0412120)   (Publisher web site)
  13. Singular Lefschetz pencils.
    (with S. K. Donaldson and L. Katzarkov)
    Geom. Topol. 9 (2005), 1043-1114.   (arXiv: math.DG/0410332)   (Publisher web site)
  14. Some open questions about symplectic 4-manifolds, singular plane curves, and braid group factorizations.
    Proc. 4th European Congress of Mathematics (Stockholm, 2004), A. Laptev Ed., European Math. Soc., 2005, 23-40.   (arXiv: math.GT/0410119)   (Publisher web site)
  15. Lagrangian submanifolds and Lefschetz pencils.
    (with V. Muñoz and F. Presas)
    J. Symplectic Geom. 3 (2005), 171-219.   (arXiv: math.SG/0407126)   (Publisher web site)
  16. Symplectic 4-manifolds, singular plane curves, and isotopy problems.
    Floer Homology, Gauge Theory, and Low Dimensional Topology (Budapest, 2004), Amer. Math. Soc., Clay Math. Proceedings 5 (2006), 263-276.   (arXiv: math.GT/0411233)
  17. Mapping class group factorizations and symplectic 4-manifolds: some open problems.
    Problems on Mapping Class Groups and Related Topics, B. Farb Ed., Amer. Math. Soc., Proc. Symp. Pure Math., 74 (2006), 123-132.
  18. Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves.
    (with L. Katzarkov and D. Orlov)
    Inventiones Math. 166 (2006), 537-582.   (arXiv: math.AG/0506166)   (Publisher web site)
  19. The canonical pencils on Horikawa surfaces.
    Geom. Topol. 10 (2006), 2173-2217.   (arXiv: math.GT/0605692)   (Publisher web site)
  20. Mirror symmetry and T-duality in the complement of an anticanonical divisor
    J. Gökova Geom. Topol. 1 (2007), 51-91.   (arXiv: 0706.3207)   (Publisher web site)
  21. Lefschetz pencils, branched covers and symplectic invariants.
    (with I. Smith)
    Symplectic 4-manifolds and algebraic surfaces (Cetraro, 2003), Springer, Lect. Notes in Math. 1938, Springer, 2008, 1-53.   (arXiv: math.SG/0401021)   (Publisher web site)
  22. A degree doubling formula for braid monodromies and Lefschetz pencils.
    (with L. Katzarkov)
    Pure Appl. Math. Q. 4 (2008), 237-318.   (arXiv: math.SG/0605001)   (Publisher web site)
  23. Mirror symmetry for weighted projective planes and their noncommutative deformations.
    (with L. Katzarkov and D. Orlov)
    Ann. Math. 167 (2008), 867-943.   (arXiv: math.AG/0404281)   (Publisher web site)
  24. Special Lagrangian fibrations, mirror symmetry and Calabi-Yau double covers.
    Géométrie différentielle, physique mathématique, mathématiques et société (I), O. Hijazi Ed., Soc. Math. Fr., Astérisque 321 (2008), 99-128.   (arXiv: 0803.2734)
  25. Special Lagrangian fibrations, wall-crossing, and mirror symmetry.
    Surveys in Differential Geometry, Vol. 13, Intl. Press, 2009, 1-47.   (arXiv: 0902.1595)
  26. La conjecture de Weinstein en dimension 3 (d'après C. H. Taubes).
    Séminaire Bourbaki, vol. 2008/09, exposé no 1002, Astérisque 332 (2010), 135-159.  
  27. Fukaya categories of symmetric products and bordered Heegaard-Floer homology.
    J. Gökova Geom. Topol. 4 (2010), 1-54.   (arXiv: 1001.4323)   (Publisher web site)
  28. Fukaya categories and bordered Heegaard-Floer homology.
    Proc. International Congress of Mathematicians (Hyderabad, 2010), Vol. II, Hindustan Book Agency, 2010, 917-941.   (arXiv: 1003.2962)
  29. Homological mirror symmetry for punctured spheres.
    (with M. Abouzaid, A. Efimov, L. Katzarkov and D. Orlov)
    J. Amer. Math. Soc. 26 (2013), 1051-1083.   (arXiv: 1103.4322)   (Publisher web site)
  30. On Khovanov-Seidel quiver algebras and bordered Floer homology.
    (with E. Grigsby and S. Wehrli)
    Selecta Math. 20 (2014), 1-55.   (arXiv: 1107.2841)   (Publisher web site)
  31. A beginner's introduction to Fukaya categories.
    Contact and Symplectic Topology, F. Bourgeois et al. Eds., Bolyai Soc. Math. Stud. 26, Springer, 2014, 85-136.   (arXiv: 1301.7056)
  32. Factorizations in SL(2,Z) and simple examples of inequivalent Stein fillings.
    J. Symplectic Geom. 13 (2015), 261-277.   (arXiv: 1311.0847)   (Publisher web site)
  33. Sutured Khovanov homology, Hochschild homology, and the Ozsváth-Szabó spectral sequence.
    (with E. Grigsby and S. Wehrli)
    Trans. Amer. Math. Soc. 367 (2015), 7103-7131.   (arXiv: 1303.1986)   (Publisher web site)
  34. Infinitely many monotone Lagrangian tori in R6.
    Inventiones Math. 201 (2015), 909-924.   (arXiv: 1407.3725)  (Publisher web site)
  35. Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces.
    (with M. Abouzaid and L. Katzarkov)
    Publ. Math. IHES 123 (2016), 199-282.   (arXiv: 1205.0053)  (Publisher web site)
  36. Speculations on homological mirror symmetry for hypersurfaces in (C*)n.
    Surveys in Differential Geometry, Vol. 22, Intl. Press, 2018, 1-47.   (arXiv: 1705.06667)
  37. Fukaya categories of surfaces, spherical objects, and mapping class groups.
    (with I. Smith)
    Forum Math. Sigma 9 (2021), e26, 1-50.   (arXiv: 2006.09689)  (Publisher web site)
  38. Homological mirror symmetry for hypersurfaces in (C*)n.
    (with M. Abouzaid)
    to appear in Geom. Topol.   (arXiv: 2111.06543)



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