Singular open book structures from real mappings

Raimundo Araújo dos Santos; Ying Chen; Mihai Tibăr

Open Mathematics (2013)

  • Volume: 11, Issue: 5, page 817-828
  • ISSN: 2391-5455

Abstract

top
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.

How to cite

top

Raimundo Araújo dos Santos, Ying Chen, and Mihai Tibăr. "Singular open book structures from real mappings." Open Mathematics 11.5 (2013): 817-828. <http://eudml.org/doc/269469>.

@article{RaimundoAraújodosSantos2013,
abstract = {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.},
author = {Raimundo Araújo dos Santos, Ying Chen, Mihai Tibăr},
journal = {Open Mathematics},
keywords = {Singularities of real analytic mappings; Open book decompositions; Milnor fibrations; singularities of real analytic mappings; open book decompositions; links of singularities; Thom's regularity condition},
language = {eng},
number = {5},
pages = {817-828},
title = {Singular open book structures from real mappings},
url = {http://eudml.org/doc/269469},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Raimundo Araújo dos Santos
AU - Ying Chen
AU - Mihai Tibăr
TI - Singular open book structures from real mappings
JO - Open Mathematics
PY - 2013
VL - 11
IS - 5
SP - 817
EP - 828
AB - 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.
LA - eng
KW - Singularities of real analytic mappings; Open book decompositions; Milnor fibrations; singularities of real analytic mappings; open book decompositions; links of singularities; Thom's regularity condition
UR - http://eudml.org/doc/269469
ER -

References

top
  1. [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 Zbl1202.32026
  2. [2] Araújo dos Santos R., Tibăr M., Real map germs and higher open books, preprint available http://arxiv.org/abs/0801.3328 Zbl1202.32026
  3. [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 Zbl1172.32008
  4. [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 Zbl1198.32013
  5. [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. [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 Zbl0377.58006
  7. [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. [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. [9] Jacquemard A., Fibrations de Milnor pour des applications réelles, C. R. Acad. Sci. Paris Sér. I Math., 1983, 296(10), 443–446 Zbl0589.32018
  10. [10] Jacquemard A., Fibrations de Milnor pour des applications réelles, Boll. Un. Mat. Ital. B, 1989, 3(3), 591–600 Zbl0729.55011
  11. [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. [12] Looijenga E., A note on polynomial isolated singularities, Indag. Math., 1971, 33, 418–421 Zbl0234.57010
  13. [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 Zbl1222.32054
  14. [14] Milnor J., Singular Points of Complex Hypersurfaces, Ann. of Math. Studies, 61, Princeton University Press, Princeton, 1968 Zbl0184.48405
  15. [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 Zbl0806.57021
  16. [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. [17] Oka M., Non-degenerate mixed functions, Kodai Math. J., 2010, 33(1), 1–62 http://dx.doi.org/10.2996/kmj/1270559157 
  18. [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 Zbl1169.32006
  19. [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 Zbl1084.32023
  20. [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 Zbl1020.32027
  21. [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 Zbl0882.32021
  22. [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. [23] Tibăr M., Polynomials and Vanishing Cycles, Cambridge Tracts in Math., 170, Cambridge University Press, Cambridge, 2007 Zbl1126.32026
  24. [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 Zbl0269.57011
  25. [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 Zbl0116.39202
  26. [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 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.