Links of singular points in complex hypersurfaces

Consider the canonical embedding of a sphere of radius \varepsilon, say S_\varepsilon^3 inside \mathbb C^2 as the set of pairs (z,w) with |z|^2+|w|^2=\varepsilon^2, and the curve X= \{(z,w):z^k + w^l =0\}. Calculate the homology of the intersection X\cap S_\varepsilon^3 for as many values of (k,l) as possible where k,l>1, with \varepsilon of your liking.

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Links of singular points in complex hypersurfaces

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