Vol. 295, No. 1, 2018

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ISSN: 0030-8730
The growth rate of the tunnel number of m-small knots

Tsuyoshi Kobayashi and Yo’av Rieck

Vol. 295 (2018), No. 1, 57–101
Abstract

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
Mathematical Subject Classification 2010
Primary: 57M25, 57M99
Milestones
Received: 18 July 2016
Revised: 4 March 2017
Accepted: 7 August 2017
Published: 13 March 2018
Authors
Tsuyoshi Kobayashi
Department of Mathematics
Nara Women’s University
Kitauoyanishi-machi, Nara 630-8506
Japan
Yo’av Rieck
Department of Mathematical Sciences
University of Arkansas
Fayetteville, AR 72701
United States