The geometry of continued fractions and the topology of surface singularities
The geometry of continued fractions and the topology of surface singularities
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连分数的几何和表面奇点的拓扑
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Patrick Popescu
中科院分区：
文献类型：
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作者：
Patrick Popescu
我们调查使用连分式展开在代数和拓扑研究复杂的解析奇点。我们还证明了新的结果，首先是关于一个几何对偶相对于平面补充锥之间的晶格，其次是关于存在一个典型的管道结构的抽象边界（也称为链接）的正常表面奇点。补充锥之间的对偶性特别给出了希尔泽布鲁赫发现的两个数l >1和l/（l - 1）的连分数展开之间的对偶性的几何解释。
We survey the use of continued fraction expansions in the algebraical and topological study of complex analytic singularities. We also prove new results, firstly concerning a geometric duality with respect to a lattice between plane supplementary cones and secondly concerning the existence of a canonical plumbing structure on the abstract boundaries (also called links) of normal surface singularities. The duality between supplementary cones gives in particular a geometric interpretation of a duality discovered by Hirzebruch between the continued fraction expansions of two numbers l >1 and l/(l - 1).