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2013 | 11 | 5 | 817-828
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Singular open book structures from real mappings

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We define open book structures with singular bindings. Starting with an extension of Milnor’s results on local fibrations for germs with nonisolated singularity, we find classes of genuine real analytic mappings which yield such open book structures.
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Bibliografia
  • [1] Araújo dos Santos R., Tibăr M., Real map germs and higher open book structures, Geom. Dedicata, 2010, 147, 177–185 http://dx.doi.org/10.1007/s10711-009-9449-z
  • [2] Araújo dos Santos R., Tibăr M., Real map germs and higher open books, preprint available http://arxiv.org/abs/0801.3328
  • [3] Cisneros-Molina J.L., Join theorem for polar weighted homogeneous singularities, In: Singularities II, Cuernavaca, January 8–26, 2007, Contemp. Math., 475, American Mathematical Society, Providence, 2008, 43–59
  • [4] Cisneros-Molina J.L., Seade J., Snoussi J., Milnor fibrations and d-regularity for real analytic singularities, Internat. J. Math., 2010, 21(4), 419–434 http://dx.doi.org/10.1142/S0129167X10006124
  • [5] Ehresmann C., Les connexions infinitésimales dans un espace fibré différentiable, In: Colloque de Topologie (Espaces Fibrés), Bruxelles, 1950, Georges Thone, Liège; Masson et Cie., Paris, 1951, 29–55
  • [6] Gibson C.G., Wirthmüller C., du Plessis A.A., Looijenga E.J.N., Topological Stability of Smooth Mappings, Lecture Notes in Math., 552, Springer, Berlin-New York, 1976 http://dx.doi.org/10.1007/BFb0095246
  • [7] Hamm H.A., Lê D.T., Un théorème de Zariski du type de Lefschetz, Ann. Sci. École Norm. Sup., 1973, 6(3), 317–355
  • [8] Hironaka H., Stratification and flatness, In: Real and Complex Singularities, Oslo, August 5–25, 1976, Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, 199–265 http://dx.doi.org/10.1007/978-94-010-1289-8_8
  • [9] Jacquemard A., Fibrations de Milnor pour des applications réelles, C. R. Acad. Sci. Paris Sér. I Math., 1983, 296(10), 443–446
  • [10] Jacquemard A., Fibrations de Milnor pour des applications réelles, Boll. Un. Mat. Ital. B, 1989, 3(3), 591–600
  • [11] Lê D.T., Some remarks on relative monodromy, In: Real and Complex Singularities, Oslo, August 5–25, 1976, Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, 397–403
  • [12] Looijenga E., A note on polynomial isolated singularities, Indag. Math., 1971, 33, 418–421
  • [13] Massey D.B., Real analytic Milnor fibrations and a strong Łojasiewicz inequality, In: Real and Complex Singularities, London Math. Soc. Lecture Note Ser., 380, Cambridge University Press, Cambridge, 2010, 268–292 http://dx.doi.org/10.1017/CBO9780511731983.020
  • [14] Milnor J., Singular Points of Complex Hypersurfaces, Ann. of Math. Studies, 61, Princeton University Press, Princeton, 1968
  • [15] Némethi A., Zaharia A., Milnor fibration at infinity, Indag. Math., 1992, 3(3), 323–335 http://dx.doi.org/10.1016/0019-3577(92)90039-N
  • [16] Oka M., Topology of polar weighted homogeneous hypersurfaces, Kodai Math. J., 2008, 31(2), 163–182 http://dx.doi.org/10.2996/kmj/1214442793
  • [17] Oka M., Non-degenerate mixed functions, Kodai Math. J., 2010, 33(1), 1–62 http://dx.doi.org/10.2996/kmj/1270559157
  • [18] Pichon A., Seade J., Fibred multilinks and singularities fḡ, Math. Ann., 2008, 342(3), 487–514 http://dx.doi.org/10.1007/s00208-008-0234-3
  • [19] Ruas M.A.S., Araújo dos Santos R.N., Real Milnor fibrations and (c)-regularity, Manuscripta Math., 2005, 117(2), 207–218 http://dx.doi.org/10.1007/s00229-005-0555-4
  • [20] Ruas M.A.S., Seade J., Verjovsky A., On real singularities with a Milnor fibration, In: Trends in Singularities, Trends Math., Birkhäuser, Basel, 2002, 191–213 http://dx.doi.org/10.1007/978-3-0348-8161-6_9
  • [21] Tibăr M., On the monodromy fibration of polynomial functions with singularities at infinity, C. R. Acad. Sci. Paris Sér. I Math., 1997, 324(9), 1031–1035 http://dx.doi.org/10.1016/S0764-4442(97)87881-0
  • [22] Tibăr M., Regularity at infinity of real and complex polynomial functions, In: Singularity Theory, Liverpool, August 18–24, 1996, London Math. Soc. Lecture Note Ser., 263, Cambridge University Press, Cambridge, 1999, 249–264
  • [23] Tibăr M., Polynomials and Vanishing Cycles, Cambridge Tracts in Math., 170, Cambridge University Press, Cambridge, 2007
  • [24] Winkelnkemper H.E., Manifolds as open books, Bull. Amer. Math. Soc., 1973, 79(1), 45–51 http://dx.doi.org/10.1090/S0002-9904-1973-13085-X
  • [25] Wolf J.A., Differentiable fibre spaces and mappings compatible with Riemannian metrics, Michigan Math. J., 1964, 11(1), 65–70 http://dx.doi.org/10.1307/mmj/1028999036
  • [26] Mini-Workshop: Topology of Real Singularities and Motivic Aspects, Oberwolfach, September 30–October 3, 2012, Oberwolfach Report No. 48/2012, Mathematisches Forschungsinstitut Oberwolfach, 2012, DOI: 10.4171/OWR/2012/48
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Bibliografia
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