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Null-homotopic knots have Property R
Published online by Cambridge University Press: 20 February 2023
Abstract
We prove that if K is a nontrivial null-homotopic knot in a closed oriented 3–manfiold Y such that $Y-K$ does not have an $S^1\times S^2$ summand, then the zero surgery on K does not have an $S^1\times S^2$ summand. This generalises a result of Hom and Lidman, who proved the case when Y is an irreducible rational homology sphere.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 175 , Issue 1 , July 2023 , pp. 217 - 223
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society
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