论文标题
无效的结节具有属性r
Null-homotopic knots have Property R
论文作者
论文摘要
我们证明，如果$ k $是封闭式$ 3 $ - manfiold $ y $中的非平凡的无效的结节，以至于$ y-y-k $没有$ s^1 \ times s^2 $ summand，那么$ k $的零外科手术就没有一个$ s $ s $ s^times s^times s^2 $ summand。这概括了HOM和LIDMAN的结果，后者证明了$ y $是不可约理性同源性领域的情况。
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.
