Knot invariants

Tunnel number

In mathematics, the tunnel number of a knot, as first defined by Bradd Clark, is a knot invariant, given by the minimal number of arcs (called tunnels) that must be added to the knot so that the complement becomes a handlebody. The tunnel number can equally be defined for links. The boundary of a regular neighbourhood of the union of the link and its tunnels forms a Heegaard splitting of the link exterior. (Wikipedia).

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Related pages

Knot (mathematics) | Crossing number (knot theory) | Knot invariant | Mathematics | Heegaard splitting | Link (knot theory) | Handlebody