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Let = (f, g):(Cn+ 1,0) (C2, 0) be a pair of holomorphic germswith no blowing up in codimension 0. (Two examples are the following: defines an isolated complete intersection singularity; g =lN where is a generic linear form with respect to f and N>0.) We study how the Milnor fibrations of the germs (:ß)= g-ß f are related to each other when (:ß)varies in P1. More precisely, we construct isotopic subfibrationsor subfibres of the Milnor fibrations of any two such germs.The proofs are based on the precise study of the subdiscs ofcomplex lines meeting a fixed complex plane curve germ transversally,generalizing Lê's work on the Cerf diagram. 2000 MathematicalSubject Classification: 32S55, 32S15, 32S30. 相似文献
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We say that an oriented contact manifold (M,ξ) is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity (X,x). In this article we prove that any three-dimensional oriented manifold admits at most one Milnor fillable contact structure up to contactomorphism. The proof is based on Milnor open books: we associate an open book decomposition of M with any holomorphic function f:(X,x)→(C,0), with isolated singularity at x and we verify that all these open books carry the contact structure ξ of (M,ξ)—generalizing results of Milnor and Giroux. 相似文献
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The abstract boundary M of a normal complex-analytic surface singularity is canonically equipped with a contact structure. We show that if M is a rational homology sphere, then this contact structure is uniquely determined by the topological type of M. An essential tool is the notion of open book carrying a contact structure, defined by E. Giroux. To cite this article: C. Caubel, P. Popescu-Pampu, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
4.
We define the contact boundary of a complex polynomial f : ℂ
n
→ ℂ as the intersection of some generic fiber with a large sphere. We show that, up to contact isotopy, this does not depend
on the choice of the fiber (provided it is generic) and is invariant under polynomial automorphism of ℂ
n
. We next prove that the formal homotopy class of this contact boundary is invariant in a large family of deformations of
polynomials, which are not necessarily topologically trivial.
Received: 15 November 2002
Published online: 20 March 2003
Mathematics Subject Classification (2000): 32S55, 53D15, 32S50 相似文献
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