Dehn surgery and satellite knots

Gordon, C. McA.

doi:10.1090/S0002-9947-1983-0682725-0

Dehn surgery and satellite knots
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by C. McA. Gordon

Trans. Amer. Math. Soc. 275 (1983), 687-708

DOI: https://doi.org/10.1090/S0002-9947-1983-0682725-0

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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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