Essential laminations and Dehn surgery on 2-bridge knots
The main result of the paper is that any nontrivial Dehn surgery on a nontorus 2-bridge knot produces a manifold which is covered by \(\mathbb{R}^3\). In particular, his manifold is irreducible and has infinite fundamental group. As a consequence, the author recovers the classical theorem of \textit{Moto-o Takahashi} [Two-bridge knots have property \(P\), Mem. Am. Math. Soc. 239 (1981; Zbl 0451.57003)] that 2-bridge knots satisfy property \(P\). The results of the paper are consequences of showing that the considered manifolds contain an essential lamination. The results of the paper were also obtained independently by \textit{Ramin Naimi} [Contemp. Math. 164, 183-186 (1994; Zbl 0819.57002)].
scientific article; zbMATH DE number 768749