The growth rate of the tunnel number of m-small knots
Tsuyoshi Kobayashi, Yo'av Rieck
TL;DR
This paper calculates the growth rate of the tunnel number for m-small knots, linking it to their bridge indices, and provides insights into the asymptotic behavior of this knot invariant.
Contribution
It introduces a formula relating the growth rate of the tunnel number of m-small knots to their bridge indices, advancing understanding of knot invariants.
Findings
Growth rate expressed in terms of bridge indices
Provides a method to compute asymptotic behavior of tunnel numbers
Enhances understanding of knot complexity measures
Abstract
In a previous paper the authors defined the growth rate of the tunnel number of knots, an invariant that measures that 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.
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