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- W2950673513 abstract "Abstract Let $K$ be a nontrivial knot in $S^3$ with the exterior $E(K)$, and $gamma in G(K) = pi _1(E(K), *)$ a slope element represented by an essential simple closed curve on $partial E(K)$ with base point $* in partial E(K)$. Since the normal closure $langle !langle gamma rangle !rangle $ of $gamma $ in $G(K)$ coincides with that of $gamma ^{-1}$, and $gamma $ and $gamma ^{-1}$ correspond to a slope $r in mathbb{Q} cup { infty }$, we write $langle !langle r rangle !rangle = langle !langle gamma rangle !rangle $. The normal closure $langle !langle r rangle !rangle $ describes elements, which are trivialized by $r$-Dehn filling of $E(K)$. In this article, we prove that $langle !langle r_1 rangle !rangle = langle !langle r_2 rangle !rangle $ if and only if $r_1 = r_2$, and for a given finite family of slopes $mathcal{S} = { r_1, dots , r_n }$, the intersection $langle !langle r_1 rangle !rangle cap cdots cap langle !langle r_n rangle !rangle $ contains infinitely many elements except when $K$ is a $(p, q)$-torus knot and $pq in mathcal{S}$. We also investigate inclusion relation among normal closures of slope elements." @default.
- W2950673513 created "2019-06-27" @default.
- W2950673513 creator A5075486332 @default.
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- W2950673513 date "2019-04-08" @default.
- W2950673513 modified "2023-10-17" @default.
- W2950673513 title "Nontrivial Elements in a Knot Group That are Trivialized by Dehn Fillings" @default.
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- W2950673513 doi "https://doi.org/10.1093/imrn/rnz069" @default.
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