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arXiv · 2201.10613

Null-homotopic knots have Property R

Yi Ni
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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 generalizes a result of Hom and Lidman, who proved the case when $Y$ is an irreducible rational homology sphere.

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Yi Ni. 2022-01-25. Null-homotopic knots have Property R. https://doi.org/10.1017/s0305004123000129

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