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Given an   n  ‐component link   L   in any 3‐manifold   M  , the space    L  ⊂    (  Q  ∪   {  ∞  }   )   nof rational surgery slopes yielding L‐spaces is already fully characterized in joint work by the author when    n    =    1    and   L   is nontrivial. For    n  >  1   , however, there are no previous results for   L   as a rational subspace, and only limited results for integer surgeries    L  ∩   Z  nonS  3    . Herein, we provide the first nontrivial explicit descriptions of   L   for rational surgeries on multi‐component links. Generalizing Hedden's and Hom's L‐space result for cables, we compute both   L  , and its topology, for all satellites by torus‐links inS  3    . For fractal‐boundaried   L   resulting from satellites by algebraic links or iterated torus links, we develop arbitrarily precise approximation tools. We also extend the provisional validity of the L‐space conjecture for rational surgeries on a knot    K  ⊂   S  3to rational surgeries on such satellite‐links of   K  . These results exploit the author's generalized Jankins–Neumann formula for graph manifolds.

Rational L‐space surgeries on satellites by algebraic links