Dehn Surgery and Satellite Knots

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Abstract
For certain kinds of $3$-manifolds, the question whether such a manifold can be obtained by nontrivial Dehn surgery on a knot in ${S^3}$ is reduced to the corresponding question for hyperbolic knots. Examples are, whether one can obtain ${S^3}$, a fake ${S^3}$, a fake ${S^3}$ with nonzero Rohlin invariant, ${S^1} \times {S^2}$, a fake ${S^1} \times {S^2}, {S^1} \times {S^2} \# M$ with $M$ nonsimply-connected, or a fake lens space.

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