Link of a singularity

Summary

The link of a singular point of a complex analytic set is its intersection with a small sphere centred at the point, see the definition. Near the point, the set is homeomorphic to the cone over its link, so the link carries the local topology of the singularity. For an isolated hypersurface singularity in $\C^{n+1}$ the link is a smooth closed manifold of dimension $2n - 1$. For plane curves it is a link in the knot theory sense, a disjoint union of circles in $S^3$.