Abstract
The paper focusses on the existence of higher open book structures defined by real map germs \({\psi : (\mathbb{R}^m ,0) \to (\mathbb{R}^p ,0)}\) such that Sing \({\psi \cap \psi^{-1}(0) \subset \{0\}}\). A general existence criterion is proved, with view to weighted-homogeneous maps.
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References
A’Campo N.: Le Nombre de Lefschetz d’une Monodromie. Indag. Math. 35, 113–118 (1973)
Church P.T., Lamotke K.: Non-trivial polynomial isolated singularities. Indag. Math. 37, 149–154 (1975)
Durfee A.: Fibered knots and algebraic singularities. Topology 13, 47–59 (1974)
dos Santos, R.: Uniform (M)-condition and strong Milnor fibrations. In: Brasselet, J.P., et al. (eds.) Singularities II: Geometric and Topological Aspects, Proc. of the Conference in honour of Lê Dũng Tráng. Cuernavaca, Mexico (2007), Contemp. Math. 475, 43–59 (2008)
dos Santos, R., Tibăr, M.: Real map germs and higher open books, manuscript, December 7, preprint arXiv:0801.3328 (2007)
Etnyre, J.B.: Lectures on open book decompositions and contact structures, Floer homology, gauge theory, and low-dimensional topology, pp. 103–141, Clay Math. Proc., 5, Amer. Math. Soc., Providence, RI (2006)
Jacquemard, A.: Thèse 3ème cycle Université de Dijon (1982)
Jacquemard, A.: Fibrations de Milnor pour des applications réelles. Boll. Un. Mat. Ital. B(7)3, no. 3, 591–600 (1989)
Lê, D.T.: Some remarks on relative monodromy, real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), pp. 397–403. Sijthoff and Noordhoff, Alphen aan den Rijn (1977)
Looijenga E.J.N.: A note on polynomial isolated singularities. Indag. Math. 33, 418–421 (1971)
Milnor, J.: Singular points of complex hypersurfaces. Ann. Math. Stud. 61, Princeton (1968)
Oka, M.: Non-degenerate mixed functions, manuscript
Ruas M.A.S., dos Santos R.: Real Milnor fibrations and C-regularity. Manuscr. Math. 117(2), 207–218 (2005)
Ruas, M.A.S., Seade, J., Verjovsky, A.: On real singularities with a Milnor fibration. In: Trends in Singularities, pp. 191–213, Trends Math., Birkhäuser, Basel (2002)
Seade J.: On Milnor’s fibration theorem for real and complex singularities in geometry and topology, pp. 127–158. World Sci. Publ., Hackensack, NJ (2007)
Tibăr, M. (2007) Polynomials and Vanishing Cycles. Cambridge Tracts in Mathematics, 170, Cambridge University Press, Cambridge, xii+253
Winkelnkemper H.E.: Manifolds as open books. Bull. Amer. Math. Soc 79, 45–51 (1973)
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Araújo dos Santos, R., Tibăr, M. Real map germs and higher open book structures. Geom Dedicata 147, 177–185 (2010). https://doi.org/10.1007/s10711-009-9449-z
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DOI: https://doi.org/10.1007/s10711-009-9449-z