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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Dehn surgery and satellite knots


Author: C. McA. Gordon
Journal: Trans. Amer. Math. Soc. 275 (1983), 687-708
MSC: Primary 57M25; Secondary 57N10
MathSciNet review: 682725
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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} \char93 M$ with $ M$ nonsimply-connected, or a fake lens space.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0682725-0
PII: S 0002-9947(1983)0682725-0
Keywords: Dehn surgery, satellite knots, simple knots
Article copyright: © Copyright 1983 American Mathematical Society