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  "body": "\n## Definition\n\nLet $V$ be a complex [[analytic set|3RWWZYPAFV]] in an open subset of $\\C^N$ and let $p \\in V$.\nFor $\\varepsilon \u003e 0$, let $S_\\varepsilon(p)$ be the [[sphere|P9CM4GQ2T0]] of radius $\\varepsilon$ centred at $p$, and let $K_\\varepsilon = V \\cap S_\\varepsilon(p)$.\nThere is $\\varepsilon_0 \u003e 0$ such that, for $0 \u003c \\varepsilon \u003c \\varepsilon' \\le \\varepsilon_0$, the spaces $K_\\varepsilon$ and $K_{\\varepsilon'}$ are [[homeomorphic|0QT00PB5G2]].\nThe *link* of $V$ at $p$ is $K_\\varepsilon$ for any such $\\varepsilon$, defined up to homeomorphism.\n\n## Remarks\n\nFor $\\varepsilon$ small, $V \\cap B_\\varepsilon(p)$, where $B_\\varepsilon(p)$ is the closed ball, is homeomorphic to the cone over $K_\\varepsilon$ with vertex $p$; this is the conic structure theorem.\nIf $V$ is smooth at $p$ of complex dimension $d$, the link is a sphere $S^{2d - 1}$.\nIf $V = f^{-1}(0) \\subset \\C^{n+1}$ with an isolated singularity at $p$, the link is a smooth closed manifold of dimension $2n - 1$, and Milnor showed that it is $(n-2)$-connected.\n\nExample: $V = \\set{x^2 = y^3} \\subset \\C^2$ at $0$.\nThe map $t \\mapsto (t^3, t^2)$ is a bijection from $\\C$ onto $V$.\nOn the sphere $S_\\varepsilon$, the points of $V$ are $(t^3, t^2)$ with $\\abs{t}$ fixed, which trace the torus knot of type $(2, 3)$, the trefoil.\n\nNon-example of the condition on $\\varepsilon$: $V = \\set{x y (y - 1) = 0} \\subset \\C^2$ at $0$.\nFor $\\varepsilon \u003c 1$, $K_\\varepsilon$ consists of the two circles cut out by $x = 0$ and $y = 0$, a Hopf link.\nFor $\\varepsilon \u003e 1$, the line $y = 1$ also meets $S_\\varepsilon$ in a third circle, so this sphere is too large to give the link.\n",
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