Alternating knots satisfy strong property P
Alternating knots satisfy strong property P
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交替结满足强性质 P
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
R. Roberts
中科院分区：
文献类型：
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作者：
Charles Delman;R. Roberts
抽象的。假设一个流形是由有限德恩手术产生的非环面交替结塞弗特的算法产生一个棋盘表面。通过证明它包含一个本质层，我们证明了这样的流形具有
$ {\Bbb R}^{3} $作为泛覆盖，因此是不可约的，有无限基本群。与以前的工作罗伯茨，谁证明了这一结果的情况下，交替结塞弗特的算法不产生一个棋盘形表面，和莫泽，谁分类的流形上的手术环面结，本文完成的证明，交替结满足强性质P。
Abstract. Suppose a manifold is produced by finite Dehn surgery on a non-torus alternating knot for which Seifert's algorithm produces a checkerboard surface. By demonstrating that it contains an essential lamination, we prove that such a manifold has
$ {\Bbb R}^{3} $ as universal cover and, consequently, is irreducible and has infinite fundamental group. Together with previous work of Roberts, who proved this result in the case of alternating knots for which Seifert's algorithm does not produce a checkerboard surface, and Moser, who classified the manifolds produced by surgery on torus knots, this paper completes the proof that alternating knots satisfy Strong Property P.