On the degeneration of tunnel numbers under a connected sum

Tao Li; Ruifeng Qiu

doi:10.1090/tran/6473

On the degeneration of tunnel numbers under a connected sum

Tao Li
, Ruifeng Qiu

数学科学学院

Boston College

科研成果: 期刊稿件 › 文章 › 同行评审

6 引用（Scopus）

摘要

We show that, for any integer n ≥ 3, there is a prime knot k such that (1) k is not meridionally primitive, and (2) for every m-bridge knot kʹ with m ≤ n, the tunnel numbers satisfy t(k#kʹ) ≤ t(k). This gives counterexamples to a conjecture of Morimoto and Moriah on tunnel numbers under a connected sum and meridionally primitive knots.

源语言	英语
页（从-至）	2793-2807
页数	15
期刊	Transactions of the American Mathematical Society
卷	368
期	4
DOI	https://doi.org/10.1090/tran/6473
出版状态	已出版 - 4月 2016

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10.1090/tran/6473

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AB - We show that, for any integer n ≥ 3, there is a prime knot k such that (1) k is not meridionally primitive, and (2) for every m-bridge knot kʹ with m ≤ n, the tunnel numbers satisfy t(k#kʹ) ≤ t(k). This gives counterexamples to a conjecture of Morimoto and Moriah on tunnel numbers under a connected sum and meridionally primitive knots.

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On the degeneration of tunnel numbers under a connected sum

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