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**Surgery on knots in solid tori.**
*(English)*
Zbl 0678.57004

R. A. Litherland [Proc. Lond. Math. Soc., III. Ser 39, 130-146 (1979; Zbl 0418.57002)] has shown that non-trivial surgeries along a sufficiently complicated sattelite knot will never yield a homotopy sphere. In the paper under review it is demonstrated how the author’s sutured manifold theory can be exploited for this problem to give a different proof of the previous result which also works for all remaining cases. In fact, it is shown that surgery along a curve in the solid torus yields an (\(\partial -)\) irreducible 3-manifold or a non-trivial connected sum, unless the knot is of a special type (completely analyzed in a yet unpublished paper by Berge).

Reviewer: K.Johannson

### MSC:

57M25 | Knots and links in the \(3\)-sphere (MSC2010) |

57N10 | Topology of general \(3\)-manifolds (MSC2010) |

57R65 | Surgery and handlebodies |