We construct infinitely many Legendrian links in the standard contact R 3 with arbitrarily many topologically distinct Lagrangian fillings. The construction is used to find links in S 3 that bound topologically distinct pieces of algebraic curves in B 4 ⊂ C 2 , is applied to find contact 3-manifolds with topologically distinct symplectic fillings, and is generalized to higher dimensions.
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