The Depth of a Knot Tunnel

Abstract

The theory of tunnel number 1 knots detailed in [4] provides a non-negative integer invariant depth(τ ) for a knot tunnel τ . We give various results related to the depth invariant. Noting that it equals the minimal number of Goda-Scharlemann-Thompson “tunnel moves” [6] needed to construct the tunnel, we calculate the number of distinct minimal sequences of… (More)

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