A topological interpretation for the polar quotients of an algebraic plane curve singularity

  • Claude Weber
Linking Phenomena And 3-Dimensional Topology
Part of the Lecture Notes in Mathematics book series (LNM, volume 1350)


Rather than a survey, this article is a guided tour into the maze of polars, organized for the benefit of topologically minded readers. It is written for a person at home with 3-dimensional topology. On the other hand, very little is assumed from the field of singularities.

To each germ of curve V at the origin of ℂ2 there is attached a pencil of curves : the pencil of polars. The topological type of its "general fiber" is a local analytic invariant of V. It is "the" polar of V. The set of contact quotients (in H. Hironaka's sense) of V with the branches of the polar is known to be an invariant of the local topological type of V. We show here how to interpret this set of polar quotients in terms of the minimal Waldhausen decomposition of the exterior of the (algebraic) link in S3 associated to V.


Intersection Number Tangent Cone Tubular Neighborhood Solid Torus Ordinary Double Point 
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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Claude Weber
    • 1
  1. 1.Section de mathématiquesUniversité de GenèveGeneve 24

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