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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Dehn surgery and satellite knots
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by C. McA. Gordon PDF
Trans. Amer. Math. Soc. 275 (1983), 687-708 Request permission

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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 275 (1983), 687-708
  • MSC: Primary 57M25; Secondary 57N10
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0682725-0
  • MathSciNet review: 682725