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- W2149117638 abstract "Let K be a knot in S3, and let K(a/b) denote the closed oriented 3-manifold obtained by a/b-Dehn surgery on K. (We parametrize the Dehn surgeries on K by ℚ ∩ {1/0} as in [9]; in particular, K(1/0) = S3.) If K is a (p, q)-cable knot, then K(pq) is always reducible (see Section 3), and it is conjectured by González-Acuña and Short in [5] that these are the only examples where Dehn surgery on a knot in S3 yields a reducible manifold. One of the results in this direction proved in [5] is that if π1 (K(a/b)) is a non-trivial free product then |b| ≤ 5. We show that this may be sharpened to the assertion in the title." @default.
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- W2149117638 date "1987-07-01" @default.
- W2149117638 modified "2023-09-23" @default.
- W2149117638 title "Only integral Dehn surgeries can yield reducible manifolds" @default.
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- W2149117638 doi "https://doi.org/10.1017/s0305004100067086" @default.
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