Vol. 295, No. 1, 2018

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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