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VOL. 46 | 2007 The geometry of continued fractions and the topology of surface singularities
Patrick Popescu-Pampu

Editor(s) Jean-Paul Brasselet, Tatsuo Suwa

Abstract

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 $\lambda \gt 1$ and $\lambda / (\lambda -1)$.

Information

Published: 1 January 2007
First available in Project Euclid: 16 December 2018

zbMATH: 1129.14046
MathSciNet: MR2342890

Digital Object Identifier: 10.2969/aspm/04610119

Subjects:
Primary: 52C05
Secondary: 14M25, 32S25, 32S50, 57N10

Rights: Copyright © 2007 Mathematical Society of Japan

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