Mathematics > Algebraic Geometry
[Submitted on 7 Sep 2009]
Title:Principal analytic link theory in homology sphere links
View PDFAbstract: For the link $M$ of a normal complex surface singularity $(X,0)$ we ask when a knot $K\subset M$ exists for which the answer to whether $K$ is the link of the zero set of some analytic germ $(X,0)\to (\mathbb C,0)$ affects the analytic structure on $(X,0)$. We show that if $M$ is an integral homology sphere then such a knot exists if and only if $M$ is not one of the Brieskorn homology spheres $M(2,3,5)$, $M(2,3,7)$, $M(2,3,11)$.
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