Rational L-space surgeries on satellites by algebraic links

摘要

Given an n-component link L in any 3-manifold M, the space L subset of(Q?{infinity})n of 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 boolean AND Zn on S3. 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 in S3. 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 subset of S3 to rational surgeries on such satellite-links of K. These results exploit the author's generalized Jankins-Neumann formula for graph manifolds.