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  "body": "\n## Summary\n\nThe link of a singular point of a complex analytic set is its intersection with a small sphere centred at the point, see the [[definition|MHGZEW6RBM]].\nNear the point, the set is homeomorphic to the cone over its link, so the link carries the local topology of the singularity.\nFor an [[isolated hypersurface singularity|VTGYEES3VS]] in $\\C^{n+1}$ the link is a smooth closed manifold of dimension $2n - 1$.\nFor plane curves it is a [[link|1A5WRCNTM3]] in the knot theory sense, a disjoint union of circles in $S^3$.\n\n## Explanations\n\n### L1 human\n\nTo see what a singular point looks like, cut the space with a tiny sphere around it and look at what is left on the sphere.\nThe space near the point is then the cone over this cut, made of rays from the point to the cut.\nFor the curve $x^2 = y^3$ in $\\C^2$, the cut is a knotted circle in the $3$-sphere, the trefoil knot.\nFor two lines crossing at a point, it is two circles that link once, the Hopf link.\n",
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