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The growth rate of
the tunnel number of m-small knots
Tsuyoshi Kobayashi and Yo’av Rieck |
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Vol. 295 (2018), No. 1, 57–101
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Abstract |
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In a previous paper, we defined the growth rate of the tunnel number of knots, an invariant that measures the asymptotic behavior of the tunnel number under connected sum. In this paper we calculate the growth rate of the tunnel number of m-small knots in terms of their bridge indices. |
Keywords
knots, 3-manifolds, Heegaard splittings, tunnel number,
growth rate
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Mathematical Subject Classification 2010
Primary: 57M25, 57M99
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Milestones
Received: 18 July 2016
Revised: 4 March 2017
Accepted: 7 August 2017
Published: 13 March 2018
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Authors |
| Tsuyoshi Kobayashi | |
| Department of Mathematics Nara Women’s University Kitauoyanishi-machi, Nara 630-8506 Japan |
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| Yo’av Rieck | |
| Department of Mathematical
Sciences University of Arkansas Fayetteville, AR 72701 United States |
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