Topological invariants of higher order for a pair of plane curve germs

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• 作者：Maugendre ; Hé ; lè ; ne
• 关键词：14B05 ; 32S05 ; 32S45 ; 57M25 ; Topological invariant ; Discriminant ; Puiseux expansion ; Seifert manifold
• 刊名：Topology and its Applications
• 出版年：2002
• 出版时间：September 15, 2002
• 年：2002
• 卷：123
• 期：2
• 页码：297-312
• 全文大小：168 K

文摘

Let (g,f) be an analytic map germ from (C²,0) into (C²,0) and denote by (u,v) the canonical coordinates in (g,f)(C²); it is (g(x,y),f(x,y))=(u,v). In [J. London Math. Soc. (2) 59 (1999) 207–226], we showed that the set constituted of the first (not necessarily characteristic) Puiseux exponent (in the (u,v)-coordinates) of each branch δ of the discriminant curve of (g,f) is a topological invariant of (g,f). Here we prove that for each branch δ there exists an integer k(δ) such that the set constituted of the first (not necessarily characteristic) k(δ) exponents of the Puiseux series in the (u,v)-coordinates of each δ is a topological invariant of (g,f). We give different ways to compute these invariants.