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Introduction

  • András Némethi
  • Ágnes Szilárd
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2037)

Abstract

The origins of the present work go back to some milestones marking the birth of singularity theory of complex dimension≥2. They include the Thesis of Hirzebruch (1950) containing, among others, the modern theory of cyclic quotient singularities; Milnor’s construction of the exotic 7-spheres as plumbed manifolds associated with “plumbing graphs”; Mumford’s article about normal surface singularities [79] stressing for the first time the close relationship of the topology with the algebra; the treatment and classification of links of singularities 10 by Hirzebruch and his students in the 1960s (especially Brieskorn and Jänich, and later their students) based on famous results on classification of manifolds by Smale, Thom, Pontrjagin, Adams, Kervaire and Milnor, and the signature theorem of Hirzebruch. Since then, and since the appearance of the very influential book [77] of Milnor in 1968, the theory of normal surface singularities and isolated hypersurface singularities produced an enormous amount of significant results. In all of them, the link of an isolated singularity plays a central role.

Keywords

Lens Space Hypersurface Singularity Monodromy Action Seifert Manifold Plane Curve Singularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.lfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

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